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

`L_(ab)=√(73)\\L_(ac)=2\\L_(bc)=√(65)`

It's a scalene triangle

Explanation:

Distance between two points

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

`\displaystyle L=√((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)=√((0-3)^2+(-1-7)^2)=√(9+64)=√(73)`

`\displaystyle L_(ac)=√((1-3)^2+(7-7)^2)=√(4+0)=2`

`\displaystyle L_(bc)=√(\left (1-0\right )^2+(7+1)^2)=√(1+64)=√(65)`

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