Question

The coordinates of the endpoints of and are A(3, 6), B(8, 7), C(3, 3), and D(8, 4). Which statement describes how and are related?
a)AB//CD
b)AB//CD, and AB bisects CD
c)AB//CD, but AB does not bisect CD
d)AB is neither parallel nor perpendicular to CD

Answer 1

B)AB//CD, and AB bisects CD

Answer 2

Answer:

The correct answer is option a.

Step-by-step explanation:

If a line passing through two points, then the slope of a line is defined as

$m=\frac{y_2-y_1}{x_2-x_1}$

The coordinates of the endpoints of are A(3, 6), B(8, 7), C(3, 3), and D(8, 4).

$m_{AB}=\frac{7-6}{8-3}=\frac{1}{5}$

$m_{CD}=\frac{4-3}{8-3}=\frac{1}{5}$

Since slope of AB and CD are same, therefore the line AB is parallel to CD because the slope of parallel lines are equal.

Two parallel lines never intersect each other, therefore AB does not intersect CD. Only option a is correct.