Question

Hey there Ms or Mr could you please help me out with this assignment? I Have determine if the figure is a parallelogram using the distance formula (Y2-Y1)^2+(X2-X1)^2, slope formula, or midpoint formula. Please help Ms or Mr.Just a heads up this isn't a quiz it's my homework assignment for today is about proving parallelograms & Rectangles on coordinate plane.

Answer 1

The figure is not a parallelogram.

Step-by-step explanation:

First, we need to draw the parallelogram. So, the figure is:

Then, we will use the slope formula to determine if the figure is a parallelogram.

It is a parallelogram if their opposites sides have the same slope. So, the slope of RS should be the same as QT and the slope of QR should be the same as TS.

The slope of a segment that goes from (x1, y1) to (x2, y2) can be calculated as:

`m=(y_2-y_1)/(x_2-x_1)`

So, the slope of RS that goes from R(1, -1) to S(1, -7) is:

It is undefined because the division by 0 is not possible.

In the same way, the slope of QT that goes from Q(-10, -2) to T(-11, -8) is:

`m=(-8-(-2))/(-11-(-10))=(-8+2)/(-11+10)=(-6)/(-1)=6`

Then, the slope of RS is distinct from the slope of QT, so the figure is not a parallelogram.