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3 months ago

What is true about △ABC? Select three options

Mathematics

2 answers:

Svet_ta [12.7K]3 months ago

5 0

Answer:

A) AB is perpendicular to AC

B) The triangle is classified as a right triangle.

C) The triangle qualifies as an isosceles triangle

Step-by-step explanation:

we understand that

the method for determining the distance between two points is as follows:

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

step 1

Calculate the distance AB

we find

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

insert values into the formula

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

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

$d_A_B=\sqrt{32}\ units$

step 2

Calculate the distance BC

we determine

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

insert values into the formula

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

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

$d_B_C=8\ units$

step 3

Calculate the distance AC

we figure out

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

apply the formula

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

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

$d_A_C=\sqrt{32}\ units$

step 4

Examine the lengths of the triangle's sides

$d_A_B=\sqrt{32}\ units$

$d_B_C=8\ units$

$d_A_C=\sqrt{32}\ units$

therefore

The triangle ABC is identified as an isosceles triangle, having two equal-length sides. It also meets the criteria for being a right triangle due to the Pythagorean theorem.

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

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

$64=32+32$

$64=64$ ----> confirms the right triangle classification.

AB is perpendicular to AC since the legs in a right triangle are at right angles to each other.

Zina [12.3K]3 months ago

3 0

Response:

A B C

Detailed explanation:

Ed2020

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