Question

Find the length of each side and then classify the triangle by sides. Only

type in the classification of triangle by sides in your answer. You will need
to graph the triangles on your own paper. A(-1, 2), B(4,2), and C(3,-1)

Answer 1

By calculating the distance between points A(-1, 2), B(4, 2), and C(3, -1), we find that two sides of the triangle are equal, meaning the triangle is an isosceles triangle.

Step-by-step explanation:

To classify the triangle formed by points A(-1, 2), B(4, 2), and C(3, -1) by its sides, we need to calculate the length of each side using the distance formula: the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates. After calculating these lengths, we can determine the type of triangle by comparing the side lengths.

First, we find the distance AB, which is simply the horizontal distance between A and B, as they share the same y-coordinate. Thus, AB = 4 - (-1) = 5 units.

Next, we calculate the distance AC using the distance formula:
AC = √[(-1 - 3)² + (2 - (-1))²] = √[(-4)² + 32] = √[16 + 9] = √25 = 5 units.

Lastly, we calculate the distance BC:
BC = √[(4 - 3)² + (2 - (-1))²] = √[1 + 32] = √[1 + 9] = √10 ≈ 3.16 units.

Since two sides AB and AC are equal, the triangle is an isosceles triangle.