Question

Given the coordinates, classify QRT by its sides. Q(-2, -1), R(1, 5), T(-8, -4).

Answer 1

The triangle QRT formed by the coordinates Q(-2, -1), R(1, 5), and T(-8, -4) is classified as a scalene triangle.

Step-by-step explanation:

To determine the classification of the triangle by its sides, we need to calculate the lengths of its three sides using the distance formula:
`\(d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)\).`

1. Calculating the length of side QR:

`\(QR = √((1 - (-2))^2 + (5 - (-1))^2)\)`

`\(QR = √(3^2 + 6^2)\)`

`\(QR = √(9 + 36)\)`

`\(QR = √(45)\)`

`\(QR \approx 6.71\)`

2. Calculating the length of side RT:

`\(RT = √((-8 - 1)^2 + (-4 - 5)^2)\)`

`\(RT = √((-9)^2 + (-9)^2)\)`

`\(RT = √(81 + 81)\)`

`\(RT = √(162)\)`

`\(RT \approx 12.73\)`

3. Calculating the length of side QT:

`\(QT = √((-8 - (-2))^2 + (-4 - (-1))^2)\)`

`\(QT = √((-6)^2 + (-3)^2)\)`

`\(QT = √(36 + 9)\)`

`\(QT = √(45)\)`

`\(QT \approx 6.71\)`

Upon calculation, the lengths of the sides are approximately 6.71, 12.73, and 6.71 units. As none of the side lengths are equal, the triangle QRT is classified as a scalene triangle. This classification indicates that no two sides of the triangle are of equal length.