Question

use the distance formula to find the lengths of each side of the triangle. then classify the triangle by its sides. A(7,3), B(-1,0), C(7,1

Answer 1

Answer:

$L_{ab}=\sqrt{73}\\L_{ac}=2\\L_{bc}=\sqrt{65}$

It's a scalene triangle

Step-by-step explanation:

Distance between two points

The distance L between the points P(a,b), Q(c,d) is computed by

$\displaystyle L=\sqrt{(d-b)^2+(c-a)^2}$

We are given 3 points A(7,3), B(-1,0), C(7,1)

Let's find all three distances

$\displaystyle L_{ab}=\sqrt{(0-3)^2+(-1-7)^2}=\sqrt{9+64}=\sqrt{73}$

$\displaystyle L_{ac}=\sqrt{(1-3)^2+(7-7)^2}=\sqrt{4+0}=2$

$\displaystyle L_{bc}=\sqrt{\left (1-0\right )^2+(7+1)^2}=\sqrt{1+64}=\sqrt{65}$

Since the three sides are different it's a scalene triangle