Question

Line l has a slope of 2. The line through which of the following pair of points is perpendicular to l?

Answer 1

Answer:

D

Step-by-step explanation:

If two lines are perpendicular, the products of their slopes will be -1. Therefore, we're looking for a line with slope of -1/2. Let's check each answer:

A: 5 - 3 / (-2 - 3) = 2 / -5    

B: 6 - 5 / 6 - 5 = 1

C: 5 - 3 / 4 - 3 = 2

D: 4 - 3 / 3 - 5 = -1/2

The answer is D.

Answer 2

The line through points ( 3,4) ( 5,3) is perpendicular to the line l , Option D is the correct answer.

What is a Straight Line Equation ?

An equation of a straight line is y = mx+c , here m is the slope and c is the y intercept

m is determined by

$\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}$

It is given that line l has slope = 2

The line perpendicular to it will have a slope such that the product is -1

So , the line perpendicular to it should have the slope = -1/2

Slope of Option A is

5 - 3 / (-2 - 3) = 2 / -5    

Slope of Option B is

6 - 5 / 6 - 5 = 1

Slope of Option C is

5 - 3 / 4 - 3 = 2

Slope of Option D is

4 - 3 / 3 - 5 = -1/2

Therefore , The line through points ( 3,4) ( 5,3) is perpendicular to the line l , Option D is the correct answer.

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