Question

what triangle is formed by the points (3,2), (4,7), and (5,6)? triangle c triangle b triangle d triangle a

Explanation:

Step1: Recall the distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $A=(3,2)$, $B=(4,7)$, $C=(5,6)$.
The distance between $A$ and $B$:
$d_{AB}=\sqrt{(4 - 3)^2+(7 - 2)^2}=\sqrt{1 + 25}=\sqrt{26}$.
The distance between $B$ and $C$:
$d_{BC}=\sqrt{(5 - 4)^2+(6 - 7)^2}=\sqrt{1+1}=\sqrt{2}$.
The distance between $C$ and $A$:
$d_{CA}=\sqrt{(3 - 5)^2+(2 - 6)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}$.
Then, plot the points $(3,2)$, $(4,7)$, $(5,6)$ on the coordinate - plane and match with the given triangles.
By plotting the points $(3,2)$, $(4,7)$, $(5,6)$ on the coordinate plane, we can see that the triangle formed is triangle $A$.

Answer:

triangle $A$