Answer
isosceles
Work Step by Step
We use the distance formula to determine what type of triangle is pictured.
The vertices of the triangle are $A(3, 3)$, $B(0, 2)$, and $C(1, -1)$.
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:
$AB = \sqrt {(0 - 3)^2 + (2 - 3)^2}$
Simplify within the parentheses:
$AB = \sqrt {(-3)^2 + (-1)^2}$
Evaluate the exponents:
$AB = \sqrt {9 + 1}$
Add what is underneath the radical:
$AB = \sqrt {10}$
Let's look at the next side, $BC$:
$BC = \sqrt {(1 - 0)^2 + (-1 - 2)^2}$
Simplify within the parentheses:
$BC = \sqrt {(1)^2 + (-3)^2}$
Evaluate the exponents:
$BC = \sqrt {1 + 9}$
Add what is underneath the radical:
$BC = \sqrt {10}$
Let's look at $CA$:
$CA = \sqrt {(1 - 3)^2 + (-1 - 3)^2}$
Simplify within the parentheses:
$CA = \sqrt {(-2)^2 + (-4)^2}$
Evaluate the exponents:
$CA = \sqrt {4 + 16}$
Add what is underneath the radical:
$CA = \sqrt {20}$
Convert $20$ into the product of a perfect square and another number:
$CA = \sqrt {(4)(5)}$
Take the square root of $4$ to simplify:
$CA = 2 \sqrt {5}$
Two sides have the same length; therefore, this triangle is isosceles.
