Question

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

Plz answer this

Answer 1

Answer:

Solution. Let m1 be the slope of the line joining the points (2, −5) and (−2, 5) and m2 be the slope of the line joining the points (6, 3) and (1, 1). Hence, the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1

Answer 2

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

$\frac{y_2-y_1}{x_2-x_1}$

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 :-

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

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

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

Slope of line 2:-

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

$=\frac{2}{5}$

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

$=\frac{-5}{2}$×$\frac{2}{5}$

$=-1$

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