I would approach this question by first looking at where the parallelogram is located, by graphing the image. I did so and drew a rough image on Paint (See attached image)

To get the part where the diagonals intersect, I would find the midpoint of the line between points (1, 3) and (5,-9) (or the other pair). The reason is a parallelogram's diagonals always bisect each other, meaning the point they intersect is always the middle of the two diagonals.

Therefore, you can find the midpoint of a diagonal, between (1, 3) and (5, -9). The midpoint theorem is ( $\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}$ .

Take the points (1, 3) and (5, -9), and fill them in.

$(\frac{1 + 5}{2} , \frac{3 - 9}{2})$

Then solve.

$(\frac{6}{2}, \frac{-6}{2})$

(3, -3)

If you'd like to check the other midpoint:

Take the points, (8, 3) and (-2, -9)

$(\frac{8 - 2}{2}, \frac{3 - 9}{2})$

Then solve.

$(\frac{6}{2} , \frac{-6}{2})$

(3, -3)

They're the same, so that answer is correct.

Hope this helps!

8 0

3 years ago

PLEASE HELP!!! I have no clue how to find the perimeter of MNP

vladimir1956 [14]

Answer:

130

Step-by-step explanation:

Triangle MNP is twice the size of triangle SRP. So 2(x+4)=5x-34.

Distribute: 2x+8=5x-34

Add 34 on both sides: 2x+42=5x

Subract 2x on both sides: 42=3x

Divide both sides by 3: 14=x

If x=14, then 5x-34

is 5(14)-34=70-34=36.

The perimeter of the triangle MNP is

MN+NP+PM.

MN is 36

NP is doubled the 22 because triangle MNP is twice the size of triangle MQS. So NP is 44.

PM is doubled the 25 because triangle MNP is twice the size of triangle QNR. So PM is 50.

The perimeter of the triangle MNP is

MN+NP+PM

=36+44+50

=130

3 0

3 years ago