Question

Hello I need help with this question

Answer 1

Rhombus

Explanation:

Apply the formula for finding distance using coordinates to find the length of the sides of the parallelogram

Given the coordinates as;

P(6,-6) , Q(1,1),R(-6,6),S(-1,-1)

Finding the lengths

The formula to apply is;

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

For PQ where you have : P(6,-6) , Q(1,1)

`d=√((1-6)^2+(1--6)^2)\\\\d=√((-5)^2+(7)^2) \\\\d=√(25+49) \\\\d=√(74) \\\\d=8.60`

You can also apply the Pythagorean relationship to get the leg distance and calculate the hypotenuse .For example to get the length of QR ;

QR² = 7²+5²

QR = √49+25

QR = 8.60

You notice all sides are equal , 8.60 units

You also notice the opposite angles are equal

This is a rhombus