Me : )

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?

the line AB and the line CD are perpendicular lines.

Explanation:

The easiest way to work this question is with a graph done at scale.

I elaborated the attached graph with the points A, B, C, and D, and the lines AB, AC, AC, and BD.

The line AB is in red, the line AC is in organe, the line CD is in green, and the line BD is in blue.

From that graph, you can discard quickly some choices, which will avoid some calculations.

The basis to answer this question are:

1) The slopes of parallel lines are equal

2) The product of the slopes of perpendicular lines is - 1, which implies that one slope is the negative inverse of the other slope.

3) Formula to calculate the slope:

slope = rise / run = Δy / Δx

So, now you can analyze each statement:

Are the line AB and line CD perpendicular?

They might be, so we must either measure the angle to check if it is 90° or calculate the slopes. I will calculate the slopes:

line AB:

slope = run / rise = (y2 - y1) / (x2 - x1) = (4 - 1) / (-2 - (-8) ) = 3 / 6 = 1 / 2

line CD:

slope = run / rise = (y2 - y1) / (x2 - x1) = (5 - (-1) ) / (- 6 - (-3) ) = 6 / (-3) = - 2

Bingo! Those slopes are perpendicular, because 1/2 * (-2) = - 1.

So, the answer to the problem is the first option: line AB and line CD are perpendicular lines.

Clearly the second option is absurd (it is the negation of the first one), the third option is also false because it is also the negation of the first one, and if you want you can calculate the slopes of the lines AC and BD, but the figure shows that they are not parallel.