Question

show that the line joining (2,-5) and (-2,5) is perpendicular to the line joining (6,3) and (1,1)
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Answer 1

Given

• A line joining (2,-5) and (-2,5) and an another line joining (6,3) and (1,1).

To show

• that the lines are perpendicular to each other.

Concept

Slope

We define slope as the tangent (tan) of the angle a line makes with x-axis. It is denoted by m.

to find slopes of a line when any of two points on the line is given :-

Let the two points be $(x_1,y_1) \:and\:(x_2,y_2)$. Then the slope of the line is given by $\dfrac{y_2-y_1}{x_2-x_1}$

Condition for two lines to be parallel :-

Two lines are parallel if their slopes are equal.

Condition for two lines to be perpendicular

Two lines are perpendicular if the product of their slope equals -1.

Calculations :-

Slope of line 1 :-

= $\dfrac{5-(-5)}{-2-2}$

= $\dfrac{10}{-4}$

= $\dfrac{-5}{2}$

Slope of line 2:-

= $\dfrac{1-3}{1-6}$

= $\dfrac{2}{5}$

Multiplying the slopes of two lines,let us see what we get :-

= $\dfrac{-5}{2} \times \dfrac{2}{5}$

= -1

Hence,the product of slopes of two lines is -1. And therefore,we can say that lines are perpendicular to each other.