Question
what is the length of the diagonal of the triangle? Round answer to the nearest hundredth, if necessary. (-3, -6), (-3,4), (-6,8), (4,8)
Answers
GPT 3.5
To find the length of the diagonal of the triangle, we need to calculate the distance between two of its vertices. Let's find the distance between the points (-3, -6) and (4, 8).
Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values from the given points:
d = √((4 - (-3))^2 + (8 - (-6))^2)
Simplifying:
d = √((4 + 3)^2 + (8 + 6)^2)
= √(7^2 + 14^2)
= √(49 + 196)
= √(245)
≈ 15.65
So, the length of the diagonal of the triangle is approximately 15.65.
Using the distance formula, the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values from the given points:
d = √((4 - (-3))^2 + (8 - (-6))^2)
Simplifying:
d = √((4 + 3)^2 + (8 + 6)^2)
= √(7^2 + 14^2)
= √(49 + 196)
= √(245)
≈ 15.65
So, the length of the diagonal of the triangle is approximately 15.65.