Chapter 5. Co-ordinate Geometry - Problem set 5 (Page 122)Find the slope of the diagonals of a quadrilateral with vertices A(1,7), B(6,3), C(0,-3) and D(-3,3)
22. Find the slope of the diagonals of a quadrilateral with vertices A(1,7), B(6,3), C(0,-3) and D(-3,3).
The quadrilateral is formed with the coordinates A(1, 7), B(6, 3), C(0, –3) and D(–3, 3).
Slope of BD = \[\frac{3 - 3}{6 + 3} = 0\]
Slope of AC = \[\frac{7 + 3}{1 - 0} = \frac{10}{1} = 10\]
Explanation:-
A quadrilateral is formed with the coordinates A(1, 7), B(6, 3), C(0, -3) and D(-3, 3). To find the slope of BD, we can use the slope formula:
slope of BD = (y2 – y1)/(x2 – x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on BD. For BD, we can take points B(6, 3) and D(-3, 3).
So, slope of BD = (3 – 3)/(6 + 3) = 0/9 = 0
To find the slope of AC, we can take points A(1, 7) and C(0, -3) and use the slope formula:
slope of AC = (-3 – 7)/(0 – 1) = (-10)/(-1) = 10
Therefore, the slope of BD is 0 and the slope of AC is 10.
Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)