Question: Is the line passing through the points (2, 3) and (-4, -5) perpendicular to the line y = 3x / 4 + 4?

A ) No
B ) Yes

Steps to derive

1 Slope of the line passing through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁) / (x₂ - x₁).

2 So, the slope of the line passing through (2, 3) and (-4, -5) = (-5-3) / (-4-2) = 4 / 3
 [Substitute x₁ = 2, y₁ = 3, x₂ = -4 and y₂ = -5 and simplify.]

3 Slope of the line y = 3x / 4 + 4 is 3 / 4.
 [Slope = coefficient of x.]

4 Product of the slopes of the two lines = 4 / 3 x 3 / 4 = 1
 [Multiply.]

5 Two lines are perpendicular, if the product of their slopes is -1.

6 The product of the slopes of the two lines is 1. So, the two lines are not perpendicular.



Hence the right answer is Option A

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