First slide

Equation of line in Straight lines

Question

The line joining the points $(2, x)$ and $(3, 1)$ is perpendicular to the line joining the points $(x, 4)$ and $(7, 5)$ . The value of $x$ is

Easy

A

2
B

3
C

4
D

7

Solution

Slope of the line joining $(2, x)$ and $(3, 1)$ is $\frac{1 - x}{3 - 2}$ and that of the line joining $(x, 4)$ and $(7, 5)$ is $\frac{5 - 4}{7 - x} .$ Since the lines are perpendicular the product of the slopes is $- 1$
$\begin{array}{l} \Rightarrow \frac{1 - x}{1} \times \frac{1}{7 - x} = - 1 \\ \Rightarrow x = 4 . \end{array}$

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