Find k if the line passing through points P(-12,-3) and Q(4, k)has slope 1 /2 .
9. Find k if the line passing through points P(-12,-3) and Q(4, k)has slope 1 /2 .
Slope = \[\frac{1}{2}\]
Given points are P(–12, –3) and Q(4, k)
Slope of PQ =
\[\frac{k + 3}{4 + 12} = \frac{1}{2}\]
\[ \Rightarrow 2k + 6 = 16\]
\[ \Rightarrow 2k = 10\]
\[ \Rightarrow k = 5\]
Explanation:-
The given problem involves finding the value of a variable based on the slope of two points. The slope of a line passing through two points can be determined by the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
Let the given points be P(-12, -3) and Q(4, k). The slope of PQ can be found by using the slope formula:
slope of PQ = (k + 3) / (4 – (-12)) = (k + 3) / 16
It is also given that the slope of PQ is 1/2. Equating these two expressions, we get:
(k + 3) / 16 = 1/2
Multiplying both sides by 16, we get:
k + 3 = 8
Subtracting 3 from both sides, we get:
k = 5
Therefore, the value of k is 5.
Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)