Answer:
rectangle
Step-by-step explanation:
L(-1, 7), M(4, 9), N(8, -1), P(3, -3)
Distance formula:
[tex] d = \sqrt{(x2 - x1)^2 + (y_2 - y_1)^2} [/tex]
LM
[tex] LM = \sqrt{(4 - (-1))^2 + (9 - 7)^2} [/tex]
[tex] LM = \sqrt{25 + 4} [/tex]
[tex] LM = \sqrt{29} [/tex]
NP
[tex] NP = \sqrt{(3 - 8)^2 + (-3 - (-1))^2} [/tex]
[tex] NP = \sqrt{25 + 4} [/tex]
[tex] NP = \sqrt{29} [/tex]
LM = NP
MN
[tex] MN = \sqrt{(8 - 4)^2 + (-1 - 9)^2} [/tex]
[tex] MN = \sqrt{16 + 100} [/tex]
[tex] MN = \sqrt{116} [/tex]
LP
[tex] LP = \sqrt{(3 - (-1))^2 + (-3 - 7)^2} [/tex]
[tex] LP = \sqrt{16 + 100} [/tex]
[tex] LP = \sqrt{116} [/tex]
MN = LP
LN
[tex] LN = \sqrt{(8 - (-1))^2 + (-1 - 7)^2} [/tex]
[tex] LN = \sqrt{81 + 64} [/tex]
[tex] LN = \sqrt{145} [/tex]
MP
[tex] MP = \sqrt{(3 - 4)^2 + (-3 - 9)^2} [/tex]
[tex] MP = \sqrt{1 + 144} [/tex]
[tex] MP = \sqrt{145} [/tex]
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
