Question

Triangle ABC has vertices at A(-5, 4), B(4, 1), and C(1, -8). Choose the terms below which correctly describe this triangle:

Answer 1

Answer:

An ISOSCELES TRIANGLE

Step-by-step explanation:

Given a triangle ABC with vertices at A(-5, 4), B(4, 1), and C(1, -8), to know the type of triangle this is, we need to find the three sides of the triangles by taking the distance between the points.

Distance between two points is expressed as:

D = √(x2-x1)²+(y2-y1)²

For side |AB|:

A(-5, 4) and B(4, 1)

|AB| = √(4-(-5))²+(1-4)²

|AB| = √9²+3²

|AB| = √90

For side |BC|

B(4, 1), and C(1, -8)

|BC| =√(1-4)²+(-8-1)²

|BC| = √3²+9²

|BC| = √90

For side |AC|:

A(-5, 4) and C(1, -8).

|AC| = √(1-(-5))²+(-8-4)²

|AC| = √6²+12²

|AC| = √36+144

|AC| = √180

Based on the distances, it is seen that side AB and BC are equal which shows that two sides of the triangle are equal. A triangle that has two of its sides to be equal is known as an ISOSCELES TRIANGLE. Therefore the term that correctly describes the triangle is an isosceles triangle.