Question

1. given the coordinates, classify △qrt by its sides. q(-2, -1), r(1, 5), t(-8, -4)

qr = √((-2 - 1)²+(-1 - 5)²)=6.2
rt = √((1 + 8)²+(5 + 4)²)=12.7
qt = √((-2 + 8)²+((-1 + 4)²)=6.7
classify: isosceles

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $QR$

For $Q(-2,-1)$ and $R(1,5)$, $QR=\sqrt{(-2 - 1)^2+(-1 - 5)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9 + 36}=\sqrt{45}\approx6.7$.

Step3: Calculate length of $RT$

For $R(1,5)$ and $T(-8,-4)$, $RT=\sqrt{(1+8)^2+(5 + 4)^2}=\sqrt{9^2+9^2}=\sqrt{81+81}=\sqrt{162}\approx12.7$.

Step4: Calculate length of $QT$

For $Q(-2,-1)$ and $T(-8,-4)$, $QT=\sqrt{(-2 + 8)^2+(-1+4)^2}=\sqrt{6^2+3^2}=\sqrt{36 + 9}=\sqrt{45}\approx6.7$.

Step5: Classify the triangle

Since two sides ($QR$ and $QT$) have approximately the same length, the triangle is isosceles.

Answer:

Isosceles