Answer:
[tex] DE = 7.3 [/tex]
[tex] EF = 10.3 [/tex]
[tex] FD = 7.3 [/tex]
∆DEF is an isosceles ∆
Step-by-step explanation:
To find the 3 side lengths of ∆DEF, use the distance formula, which is given as [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex].
Distance between D(-2, 3) and E(5, 5):
[tex] DE = \sqrt{(5 -(-2))^2 + (5 - 3)^2} [/tex]
[tex] DE = \sqrt{(7)^2 + (2)^2} [/tex]
[tex] DE = \sqrt{49 + 4} [/tex]
[tex] DE = \sqrt{53} [/tex]
[tex] DE = 7.3 [/tex] (nearest tenth)
Distance between E(5, 5) and F(-4, 10):
[tex] EF = \sqrt{(-4 - 5)^2 + (10 - 5)^2} [/tex]
[tex] EF = \sqrt{(-9)^2 + (5)^2} [/tex]
[tex] EF = \sqrt{81 + 25} [/tex]
[tex] EF = \sqrt{106} [/tex]
[tex] EF = 10.3 [/tex] (nearest tenth)
Distance between F(-4, 10) and D(-2, 3):
[tex] FD = \sqrt{(-2 -(-4))^2 + (3 - 10)^2} [/tex]
[tex] FD = \sqrt{(2)^2 + (-7)^2} [/tex]
[tex] FD = \sqrt{4 + 49} [/tex]
[tex] FD = \sqrt{53} [/tex]
[tex] FD = 7.3 [/tex] (nearest tenth)
∆DEF has two equal sides, DE and FD. Therefore, ∆DEF can be classified as an isosceles triangle.
