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. A, B,C, AND D LIE ON THE SAME LINE
B. LINE AB AND LINE CD ARE PERPENDICULAR
C. LINE AB AND LINE CD ARE PARALLEL LINES
D. LINE AB AND LINE CD ARE INTERSECTING LINES BUT ARE NOT PERPENDICULAR
E. LINE AC AND LINE BD ARE PARALLEL LINES

Answer 1

Answer:

Option B is correct.

Step-by-step explanation:

To check if the lines are parallel or perpendicular, we need to find the slope of lines AB and CD

A=(-8,1), B= (-2,4), C= (-3, -1), and D= (-6,5)

Slope of AB = y₂-y₁/x₂-x₁

Slope of AB = 4-1/-2-(-8)

Slope of AB = 3/-2+8

Slope of AB = 3/6

Slope of AB = 1/2

Slope of CD = y₂-y₁/x₂-x₁

Slope of CD = 5+1/-6-(-3)

Slope of CD = 6/-6+3

Slope of CD = 6/-3

Slope of CD = -2

Lines are parallel if Slope of AB = Slope of CD

Lines are perpendicular if Slope of Ab = -1/Slope of CD

So, Slope of AB = 1/2

Slope of CD = -2

So, LINE AB AND LINE CD ARE PERPENDICULAR

Option B is correct.