Question

ΔSTU is located at S (−3, 0), T (0, −3), and U (3, −3). Which statement correctly classifies ΔSTU?

Answer 1

Answer:

ΔSTU is a scalene triangle

Step-by-step explanation:

Given triangle ∆STU with location of its vertices at S (−3, 0), T (0, −3), and U (3, −3). Before we can classify the type of the triangle, we need to know the value of each side of the triangle by taking the distance between the points.

Distance between two points is expressed as shown:

D = √(x2-x1)²+(y2-y1)²

For side ST,

S(-3,0) and T(0,-3)

x1 = -3, y1 = 0, x2 = 0, y2 = -3

|ST| = √{0-(-3)}²+(-3-0)²

|ST| = √3²+3²

|ST| = √18

For side SU:

S(-3,0) and U(3,-3)

x1 = -3, y1 = 0, x2 = 3, y2 = -3

|SU| = √{3-(-3)}²+(-3-0)²

|SU| = √6²+3²

|SU| = √45

For side TU:

T(0,-3) and U(3,-3)

x1 = 0, y1 = -3, x2 = 3, y2 = -3

|TU| = √{3-0}²+(-3-(-3))²

|TU| = √3²+0²

|TU| = √9

|TU| = 3

Since all the sides of the triangle are different, therefore the ∆STU is a scalene triangle