Text Book Solution
Practice Set 5.1
Practice Set 5.1 | Q 1.1 | Page 107
Find the distance between the following pair of point.
A(2, 3), B(4, 1)
Practice Set 5.1 | Q 1.2 | Page 107
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
Practice Set 5.1 | Q 1.3 | Page 107
Find the distance between the following pair of points.
R(0, -3), S(0, 5/2)
Practice Set 5.1 | Q 1.4 | Page 107
Find the distance between each of the following pairs of points.
L(5, –8), M(–7, –3)
Practice Set 5.1 | Q 1.5 | Page 107
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Practice Set 5.1 | Q 1.6 | Page 107
W( -7 / 2 , 4), X(11, 4)
Practice Set 5.1 | Q 2.1 | Page 107
Determine whether the point is collinear.
A(1, –3), B(2, –5), C(–4, 7)
Practice Set 5.1 | Q 2.2 | Page 107
Determine whether the point is collinear.
L(–2, 3), M(1, –3), N(5, 4)
Practice Set 5.1 | Q 2.3 | Page 107
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Practice Set 5.1 | Q 2.4 | Page 107
Determine whether the point is collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Practice Set 5.1 | Q 3 | Page 107
Find the point on the X–axis which is equidistant from A(–3, 4) and B(1, –4).
Practice Set 5.1 | Q 4 | Page 107
Verify that points P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.
Practice Set 5.1 | Q 5 | Page 108
Show that points P(2, –2), Q(7, 3), R(11, –1) and S (6, –6) are vertices of a parallelogram.
Practice Set 5.1 | Q 6 | Page 108
Show that points A(–4, –7), B(–1, 2), C(8, 5) and D(5, –4) are vertices of a rhombus ABCD.
Practice Set 5.1 | Q 7 | Page 108
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Practice Set 5.1 | Q 8 | Page 108
Show that the points A(1, 2), B(1, 6), C(1 + 2√3, 4) are vertices of an equilateral triangle.
Practice Set 5.2
Practice Set 5.2 | Q 1 | Page 115
Find the coordinates of point P if P divides the line segment joining the points A(–1,7) and B(4,–3) in the ratio 2 : 3.
Practice Set 5.2 | Q 2.1 | Page 115
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–3, 7), Q(1, –4), a : b = 2 : 1
Practice Set 5.2 | Q 2.2 | Page 115
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–2, –5), Q(4, 3), a : b = 3 : 4
Practice Set 5.2 | Q 2.3 | Page 115
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(2, 6), Q(–4, 1), a : b = 1 : 2
Practice Set 5.2 | Q 3 | Page 115
Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).
Practice Set 5.2 | Q 4 | Page 115
Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.
Practice Set 5.2 | Q 5 | Page 115
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k ?
Practice Set 5.2 | Q 6 | Page 115
Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).
Practice Set 5.2 | Q 7.1 | Page 115
Find the centroid of the triangle whose vertice is given below.
(–7, 6), (2, –2), (8, 5)
Practice Set 5.2 | Q 7.2 | Page 115
Find the centroid of the triangle whose vertice is given below.
(3, –5), (4, 3), (11, –4)
Practice Set 5.2 | Q 7.3 | Page 115
Find the centroid of the triangle whose vertice is given below.
(4, 7), (8, 4), (7, 11)
Practice Set 5.2 | Q 8 | Page 116
In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.
Practice Set 5.2 | Q 9 | Page 116
A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.
Practice Set 5.2 | Q 10 | Page 116
Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(–4, –8).
Practice Set 5.2 | Q 11 | Page 116
If A (–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
Practice Set 5.2 | Q 12 | Page 116
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
Practice Set 5.3
Practice Set 5.3 | Q 1.1 | Page 121
Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.
45°
Practice Set 5.3 | Q 1.2 | Page 121
Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.
60°
Practice Set 5.3 | Q 1.3 | Page 121
Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.
90°
Practice Set 5.3 | Q 2.1 | Page 121
Find the slope of the lines passing through the given point.
A(2, 3), B(4, 7)
Practice Set 5.3 | Q 2.2 | Page 121
Find the slope of the lines passing through the given point.
P (–3, 1) , Q (5, –2)
Practice Set 5.3 | Q 2.3 | Page 121
Find the slope of the lines passing through the given point.
C (5, –2) , D (7, 3)
Practice Set 5.3 | Q 2.4 | Page 121
Find the slope of the lines passing through the given point.
L (–2, –3) , M (–6, –8)
Practice Set 5.3 | Q 2.5 | Page 121
Find the slope of the lines passing through the given point.
E(–4, –2) , F (6, 3)
Practice Set 5.3 | Q 2.6 | Page 121
Find the slope of the lines passing through the given point.
T (0, –3) , S (0, 4)
Practice Set 5.3 | Q 3.1 | Page 121
Determine whether the following point is collinear.
A(–1, –1), B(0, 1), C(1, 3)
Practice Set 5.3 | Q 3.2 | Page 121
Determine whether the following point is collinear.
D(–2, –3), E(1, 0), F(2, 1)
Practice Set 5.3 | Q 3.3 | Page 121
Determine whether the following point is collinear.
L(2, 5), M(3, 3), N(5, 1)
Practice Set 5.3 | Q 3.4 | Page 121
Determine whether the following point is collinear.
P(2, –5), Q(1, –3), R(–2, 3)
Practice Set 5.3 | Q 3.5 | Page 121
Determine whether the following point is collinear.
R(1, –4), S(–2, 2), T(–3, 4)
Practice Set 5.3 | Q 3.6 | Page 121
Determine whether the following point is collinear.
A(–4, 4), [Kleft( – 2, frac{5}{2} right),] N (4, –2)
Practice Set 5.3 | Q 4 | Page 121
If A (1, –1), B (0, 4), C (–5, 3) are vertices of a triangle then find the slope of each side.
Practice Set 5.3 | Q 5 | Page 121
Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.
Practice Set 5.3 | Q 6 | Page 122
Find k, if R(1, –1), S (–2, k) and slope of line RS is –2.
Practice Set 5.3 | Q 7 | Page 122
Find k, if B(k, –5), C (1, 2) and slope of the line is 7.
Practice Set 5.3 | Q 8 | Page 122
Find k, if PQ || RS and P(2, 4), Q (3, 6), R(3, 1), S(5, k)
Problem Set 5
Problem Set 5 | Q 1.1 | Page 122
Fill in the blank using correct alternative.
Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co–ordinates of point B can be …….. .
- (3,1)
- (5,3)
- (3,0)
- (1,–3)
Problem Set 5 | Q 1.2 | Page 122
Fill in the blank using correct alternative.
Out of the following, point …….. lies to the right of the origin on X– axis.
- (–2,0)
- (0,2)
- (2,3)
- (2,0)
Problem Set 5 | Q 1.3 | Page 122
Fill in the blank using correct alternative.
Distance of point (–3, 4) from the origin is ______.
- 7
- 1
- 5
- −5
Problem Set 5 | Q 1.4 | Page 122
Fill in the blank using correct alternative.
A line makes an angle of 30° with the positive direction of X– axis. So the slope of the line is ………. .
[frac{1}{2}] [frac{sqrt{3}}{2}] [frac{1}{sqrt{3}}] [sqrt{3}]
Problem Set 5 | Q 2.1 | Page 122
Determine whether the given point is collinear.
A(0,2), B(1,–0.5), C(2,–3)
Problem Set 5 | Q 2.2 | Page 122
Determine whether the given point is collinear.
[Pleft( 1, 2 right), Qleft( 2, frac{8}{5} right), Rleft( 3, frac{6}{5} right)]
Problem Set 5 | Q 2.3 | Page 122
Determine whether the given point is collinear.
L(1,2), M(5,3) , N(8,6)
Problem Set 5 | Q 3 | Page 122
Find the coordinates of the midpoint of the line segment joining P(0,6) and Q(12,20).
Problem Set 5 | Q 4 | Page 122
Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis.
Problem Set 5 | Q 5 | Page 122
Find the point on X–axis which is equidistant from P(2,–5) and Q(–2,
Problem Set 5 | Q 6.1 | Page 122
Find the distances between the following point.
A(a, 0), B(0, a)
Problem Set 5 | Q 6.2 | Page 122
Find the distances between the following point.
P(–6, –3), Q(–1, 9)
Problem Set 5 | Q 6.3 | Page 122
Find the distances between the following point.
R(–3a, a), S(a, –2a)
Problem Set 5 | Q 7 | Page 122
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
Problem Set 5 | Q 8.1 | Page 123
In the following example, can the segment joining the given point form a triangle? If a triangle is formed, state the type of the triangle considering the side of the triangle.
L(6, 4), M(–5, –3), N(–6, 8)
Problem Set 5 | Q 8.2 | Page 123
In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle.
P(–2,–6) , Q(–4,–2), R(–5,0)
Problem Set 5 | Q 8.3 | Page 123
In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle.
[Aleft( sqrt{2} , sqrt{2} right), Bleft(-sqrt{2} , -sqrt{2} right), Cleft( -sqrt{6} , sqrt{6} right)]
Problem Set 5 | Q 9 | Page 123
Find k if the line passing through points P(–12, –3) and Q(4, k) has slope
[frac{1}{2}].
Problem Set 5 | Q 10 | Page 123
Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the line joining the points C(2, 4) and D(1, 7).
Problem Set 5 | Q 11 | Page 123
Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram.
Problem Set 5 | Q 12 | Page 123
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle .
Problem Set 5 | Q 13 | Page 123
Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).
Problem Set 5 | Q 14 | Page 123
Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.
Problem Set 5 | Q 15 | Page 123
Show that A(4, –1), B(6, 0), C(7, –2) and D(5, –3) are vertices of a square.
Problem Set 5 | Q 16 | Page 123
Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
Problem Set 5 | Q 17 | Page 123
Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.
Problem Set 5 | Q 18 | Page 123
Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.
Problem Set 5 | Q 19 | Page 123
The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.
Problem Set 5 | Q 20 | Page 123
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
Problem Set 5 | Q 21 | Page 123
Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).
Problem Set 5 | Q 22 | Page 123
Find the slope of the diagonals of a quadrilateral with vertices A(1, 7), B(6, 3), C(0, –3) and D(–3, 3).