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 $A(-1, 1)$, $B(-1, -2)$, and $C(3, -2)$.
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:
$AB = \sqrt {(-1 - (-1))^2 + (-2 - 1)^2}$
Simplify within the parentheses:
$AB = \sqrt {(0)^2 + (-3)^2}$
Evaluate the exponents:
$AB = \sqrt {0 + 9}$
Add what is underneath the radical:
$AB = \sqrt {9}$
Take the square root of $9$ to simplify:
$AB = 3$
Let's look at the next side, $BC$:
$BC = \sqrt {(3 - (-1))^2 + (-2 - (-2))^2}$
Simplify within the parentheses:
$BC = \sqrt {(4)^2 + (0)^2}$
Evaluate the exponents:
$BC = \sqrt {16 + 0}$
Add what is underneath the radical:
$BC = \sqrt {16}$
Take the square root of $16$ to simplify:
$BC = 4$
Let's look at $CA$:
$CA = \sqrt {(3 - (-1))^2 + (-2 - 1)^2}$
Simplify within the parentheses:
$CA = \sqrt {(4)^2 + (-3)^2}$
Evaluate the exponents:
$CA = \sqrt {16 + 9}$
Add what is underneath the radical:
$CA = \sqrt {25}$
Take the square root of $25$:
$CA = 5$
All sides are of different lengths; therefore, this triangle is scalene.
