Question

Find the measures of the sides of AABC with vertices A(1, 3), B(5,-2),

and C(0, -4). Classify the triangle by its sides.
A. scalene
B. isosceles
C. equilateral
D. cannot be determined

Answer 1

The measures of the sides of the triangle ABC are AB = sqrt(41), BC = sqrt(29), and AC = sqrt(50). The triangle is classified as scalene.

Step-by-step explanation:

To find the measures of the sides of triangle ABC, we need to calculate the lengths of the sides AB, BC, and AC. We can use the distance formula to do this. The distance formula is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points determining the side.

Using the distance formula, we can calculate:

AB = sqrt((5 - 1)^2 + (-2 - 3)^2) = sqrt(4^2 + (-5)^2) = sqrt(16 + 25) = sqrt(41)

BC = sqrt((0 - 5)^2 + (-4 - -2)^2) = sqrt((-5)^2 + (-2)^2) = sqrt(25 + 4) = sqrt(29)

AC = sqrt((0 - 1)^2 + (-4 - 3)^2) = sqrt((-1)^2 + (-7)^2) = sqrt(1 + 49) = sqrt(50)

Since all three sides have different lengths, the triangle is classified as scalene.