Question

triangle abc has the following vertices:

• a(7, -2)
• b(-1, -8)
• c(5, 0)

is triangle abc an isosceles triangle, and why?
choose 1 answer:
a yes, because ab = bc.
b yes, because ac = bc.
c no, because (overline{ac}) is longer than (overline{ab}).
d no, because △abc doesnt have a pair of sides with equal lengths.

Explanation:

Step1: Use 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 $AB$

For points $A(7,-2)$ and $B(-1,-8)$,

$$
LATEXBLOCK0
$$

Step3: Calculate length of $BC$

For points $B(-1,-8)$ and $C(5,0)$,

$$
LATEXBLOCK1
$$

Step4: Calculate length of $AC$

For points $A(7,-2)$ and $C(5,0)$,

$$
LATEXBLOCK2
$$

Since $AB = BC=10$, triangle $ABC$ is an isosceles triangle.

Answer:

A. Yes, because $AB = BC$.