Question

if W(-10, 4), X(-3, -1), and Y(-5, 11) classify triangle WXY by its sides

Answer 1

Answer:

As the lengths of the two sides is equal. i.e. WY =  WX $=\sqrt{74}$. Therefore, the  triangle WXY is an isosceles triangle.

Step-by-step explanation:

Considering the triangle with the vertices

• W(-10, 4)

• X(-3, -1)

• Y(-5, 11)

The distance between the W(-10, 4) and Y(-5, 11) is the length of the side WY.

So,

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$\mathrm{The\:distance\:between\:}\left(-10,\:4\right)\mathrm{\:and\:}\left(-5,\:11\right)\mathrm{\:is\:}$

$=\sqrt{\left(-5-\left(-10\right)\right)^2+\left(11-4\right)^2}$

$=\sqrt{\left(-5+10\right)^2+\left(11-4\right)^2}$

$=\sqrt{5^2+7^2}$

$=\sqrt{5^2+7^2}$

$=\sqrt{74}$

So, the length of the side WY $=\sqrt{74}$.

Similarly,

The distance between the W(-10, 4) and X(-3, -1) is the length of the side WX.

$\mathrm{The\:distance\:between\:}\left(-10,\:4\right)\mathrm{\:and\:}\left(-3,\:-1\right)\mathrm{\:is\:}$

$=\sqrt{\left(-3-\left(-10\right)\right)^2+\left(-1-4\right)^2}$

$=\sqrt{\left(-3+10\right)^2+\left(-1-4\right)^2}$

$=\sqrt{49+5^2}$

$=\sqrt{49+25}$

$=\sqrt{74}$

So, the length of the side WX $=\sqrt{74}$.

As the lengths of the two sides is equal. i.e. WY =  WX $=\sqrt{74}$. Therefore, the  triangle WXY is an isosceles triangle.