Question

which of the following is the correct classification of △wxy given w(-7,1), x(0,-4), and y(2,3)? isosceles scalene none of the above equilateral

Explanation:

Step1: Recall distance formula

The distance formula 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 $WX$

For $W(-7,1)$ and $X(0, - 4)$, $d_{WX}=\sqrt{(0 + 7)^2+(-4 - 1)^2}=\sqrt{49 + 25}=\sqrt{74}$.

Step3: Calculate length of $XY$

For $X(0,-4)$ and $Y(2,-3)$, $d_{XY}=\sqrt{(2 - 0)^2+(-3 + 4)^2}=\sqrt{4+1}=\sqrt{5}$.

Step4: Calculate length of $WY$

For $W(-7,1)$ and $Y(2,-3)$, $d_{WY}=\sqrt{(2 + 7)^2+(-3 - 1)^2}=\sqrt{81 + 16}=\sqrt{97}$.

Step5: Analyze triangle type

Since all three side - lengths $\sqrt{74}$, $\sqrt{5}$, and $\sqrt{97}$ are different, the triangle is scalene.

Answer:

Scalene