Answer
scalene
Work Step by Step
We use the distance formula to determine what type of triangle is pictured.
The vertices of the triangle are $A(-2, 3)$, $B(2, 2)$, and $C(-2, -1)$.
The distance formula is given by the following formula:
$d = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Let's determine the lengths of the different sides of the triangle. We'll look at $AB$ first:
$AB = \sqrt {(2 - (-2))^2 + (2 - 3)^2}$
Simplify within the parentheses:
$AB = \sqrt {(4)^2 + (-1)^2}$
Evaluate the exponents:
$AB = \sqrt {16 + 1}$
Add what is underneath the radical:
$AB = \sqrt {17}$
Let's look at the next side, $BC$:
$BC = \sqrt {(-2 - 2)^2 + (-1 - 2))^2}$
Simplify within the parentheses:
$BC = \sqrt {(-4)^2 + (-3)^2}$
Evaluate the exponents:
$BC = \sqrt {16 + 9}$
Add what is underneath the radical:
$BC = \sqrt {25}$
Evaluate to solve:
$BC = 5$
Let's look at $CA$:
$CA = \sqrt {(-2 - (-2))^2 + (-1 - 3)^2}$
Simplify within the parentheses:
$CA = \sqrt {(0)^2 + (-4)^2}$
Evaluate the exponents:
$CA = \sqrt {0 + 16}$
Add what is underneath the radical:
$CA = \sqrt {16}$
Evaluate to solve:
$CA = 4$
All three sides have different lengths; therefore, this triangle is scalene.
