Hushar Mulga
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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 .

Solution

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)