Question

What is true about △ABC? Select three options

Answer 1

Answer:

A) AB ⊥ AC

B) The triangle is a right triangle.

C) The triangle is an isosceles triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

we have

$A(-1,3), B(-5,-1)$

substitute in the formula

$d=\sqrt{(-1-3)^{2}+(-5+1)^{2}}$

$d=\sqrt{(-4)^{2}+(-4)^{2}}$

$d_A_B=\sqrt{32}\ units$

step 2

Find the distance BC

we have

$B(-5,-1),C(3,-1)$

substitute in the formula

$d=\sqrt{(-1+1)^{2}+(3+5)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$d_B_C=8\ units$

step 3

Find the distance AC

we have

$A(-1,3),C(3,-1)$

substitute in the formula

$d=\sqrt{(-1-3)^{2}+(3+1)^{2}}$

$d=\sqrt{(-4)^{2}+(4)^{2}}$

$d_A_C=\sqrt{32}\ units$

step 4

Compare the length sides of triangle

$d_A_B=\sqrt{32}\ units$

$d_B_C=8\ units$

$d_A_C=\sqrt{32}\ units$

therefore

The triangle ABC is an isosceles triangle, because has two equal sides

The triangle ABC is a right triangle because satisfy the Pythagoras theorem

$BC^2=AB^2+AC^2$

$8^2=(\sqrt{32})^2+(\sqrt{32})^2$

$64=32+32$

$64=64$ ----> is true (Is a right triangle)

AB ⊥ AC because in a right triangle the legs are perpendicular

Answer 2

Answer:

A B C

Step-by-step explanation:

Ed2020