Question

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and
F(4, -1)?

Answer 1

To have a better visualization, you have to graph the points by hand or by using a software like MS Excel. By graphing, you will see that the triangle being formed is a right triangle. This is because a right angle is being formed by angle DEF. Hope this answers the question.

Answer 2

DEF is a right angle triangle.

Explanation:

Given: Three coordinate of triangle. D(7, 3), E(8, 1), and F(4, -1)

Using distance formula to find the length of side of triangle.

`DE=√((8-7)^2+(1-3)^2)=√(5)`

`EF=√((8-4)^2+(1+1)^2)=2√(5)`

`DF=√((4-7)^2+(1+3)^2)=5`

DE≠DF≠EF

Thus, DEF is neither equilateral nor isosceles.

Using pythagoreous theorem,

`DF^2=DE^2+EF^2`

`5^2=(√(5))^2+(2√(5))^2`

`25=25`

LHS = RHS

So, Triangle DEF is satisfy the pythagoreous theorem.

Thus, DEF is a right angle triangle.