Question

What is the answer to these

Answer 1

rectangle

Explanation:

L(-1, 7), M(4, 9), N(8, -1), P(3, -3)

Distance formula:

`d = √((x2 - x1)^2 + (y_2 - y_1)^2)`

LM

`LM = √((4 - (-1))^2 + (9 - 7)^2)`

`LM = √(25 + 4)`

`LM = √(29)`

NP

`NP = √((3 - 8)^2 + (-3 - (-1))^2)`

`NP = √(25 + 4)`

`NP = √(29)`

LM = NP

MN

`MN = √((8 - 4)^2 + (-1 - 9)^2)`

`MN = √(16 + 100)`

`MN = √(116)`

LP

`LP = √((3 - (-1))^2 + (-3 - 7)^2)`

`LP = √(16 + 100)`

`LP = √(116)`

MN = LP

LN

`LN = √((8 - (-1))^2 + (-1 - 7)^2)`

`LN = √(81 + 64)`

`LN = √(145)`

MP

`MP = √((3 - 4)^2 + (-3 - 9)^2)`

`MP = √(1 + 144)`

`MP = √(145)`

LN = MP

Opposite sides LM and NP are congruent.

Opposite sides LP and MN are congruent.

All sides are not congruent.

This quadrilateral is a parallelogram since it has two pairs of opposite congruent sides. All sides are not congruent, so it is not a square or a rhombus. Since the two diagonals are congruent, this parallelogram is also a rectangle.

Answer: rectangle