Question

I need helppp asapp, please and AND explain how you got the asnwer so i can unserstand it pleaseeee.

Answer 1

Answer:

(5, 4)

Step-by-step explanation:

We know that opposite sides of a parallelogram are parallel and congruent.

This means that when graphed on a coordinate plane, a parallelogram's opposite sides will have the same slope.

We can calculate the left side's slope using the equation:

${\rm slope}=\dfrac{y_2-y_1 \ \ {\rm (rise)}}{x_2 - x_1 \ \ {\rm (run)}}$

Plugging in the given vertices:

• (-5, 2)  ...   $(x_2, y_2)$
• (-7, -4) ...   $(x_1, y_1)$

↓↓↓

$\rm slope = \dfrac{2-(-4)}{-5 - (-7)}$

$\rm slope = \dfrac{2+4}{7 - 5}$

$\rm slope = \dfrac{6}{2}$

We could simplify this slope to 3, but for this problem it's actually more helpful to leave the fraction unsimplified because:

• The numerator tells us how many y-spaces the upper vertex is from the lower vertex.
• The denominator tells us how many x-spaces the upper vertex is from the lower vertex.

So, we know that:

• change in y = 6
• change in x = 2

Adding these to the lower right vertex which connects to the upper right vertex (which is what we are solving for), we get:

$(3, -2) + \langle 2, 6\rangle = (3 + 2, \ -2 + 6)$

$= \boxed{(5, 4)}$

So, the coordinates of the upper right vertex are (5, 4).