Question

A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. Which sentence about the points is true?
A, B, C, and D lie on the same line.
 and  are perpendicular lines.
 and  are parallel lines.
 and  are intersecting lines but are not perpendicular.
 and  are parallel lines.

Answer 1

Answer with explanation:

The Coordinates of point ,  A, B, C, and D are (-8, 1), (-2, 4), (-3, -1), and (-6, 5).

Slope between two points is given by

             $(x_{1},y_{1}),\text{and},(x_{2},y_{2}) \text{is},=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text{Slope of AB}=\frac{4-1}{-2+8}\\\\=\frac{3}{6}=\frac{1}{2}\\\\\text{Slope of CB}=\frac{4+1}{-2+3}\\\\=\frac{5}{1}=5\\\\\text{Slope of CD}=\frac{5+1}{-6+3}\\\\=\frac{6}{-3}=-2\\\\\text{Slope of AD}=\frac{5-1}{-6+8}\\\\=\frac{4}{2}=2\\\\\text{Slope of DB}=\frac{4-5}{-2+6}\\\\=\frac{-1}{4}\\\\\text{Slope of AC}=\frac{1+1}{-8+3}\\\\=\frac{2}{5}$

Coming at the Options

 1. Option 1 , is not true, because points, A, B, C and D are not collinear.

2. Slope of AB × Slope of CD

              $=\frac{1}{2} \times -2\\\\-1$

So, lines AB and CD are Perpendicular.

3. None, of the lines are parallel, as the slopes of two distinct lines are not equal.

4. None of the lines are parallel, So, all of the lines, AB, BC, CD, DA,AC, and B D are Intersecting.      

Answer 2

Line AB is perpendicular to CD.. Hope that helps.