Question

Graph parallelogram ABCD on a coordinate plane with vertices A(3,4) B(6,1) C(0,-2) and D(-3,1).

Find the slope of each side.
What do you notice about the slopes?

Answer 1

SLOPES

AB = (1 - 4) / (6 - 3) = -3 / 3 = -1
BC = (-2 - 1) / (0 - 6) = -3 / -6 = 1/2
CD = (1 - (-2)) / (-3 - 0) = 3 / -3 = -1
DA = (4 - 1) / (3 - (-3)) = 3 / 6 = 1/2

Step-by-step explanation

Every line has one side parallel to it and I know this because the slope is equal.

Answer 2

A parallelogram, the opposite sides have equal slopes.

To graph the parallelogram ABCD on a coordinate plane, we can plot the given points A(3,4), B(6,1), C(0,-2), and D(-3,1), and then connect them in order to form the parallelogram.

Here are the steps to find the slope of each side:

Plot the Points:

Plot the points A(3,4), B(6,1), C(0,-2), and D(-3,1) on the coordinate plane.

Connect the Points:

Connect the points in order (A to B to C to D to A) to form the parallelogram.

Find the Slope:

The slope of a line passing through two points

(x_1 ,y_1 ) and (x_2 ,y_2 ) is given by the formula m= y_2 -y_1/ x_2- x_1

​Calculate the slope for each pair of consecutive points:

Slope of AB: mAB​ = 1−4/6−3

​Slope of BC: mBC = −2−1/0−6

​Slope of CD: mCD = 1−(−2)/−3−0

​Slope of DA: mDA = 4−1/ 3−(−3)

​Now, observe the slopes:

mAB and mCD

​are the slopes of opposite sides. They should be equal for a parallelogram.

mBC and mDA are the slopes of the other pair of opposite sides. They should also be equal for a parallelogram.

So, for a parallelogram, the opposite sides have equal slopes.