Question

please help!!!

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

a.)equilateral triangle
b.)isosceles triangle
c.)right triangle
d.)acute scalene triangle
e.)obtuse scalene triangle

Answer 1

use distance formula to find the lenghts of sides:

\[\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

Answer 2

im lost on how to do that?

Answer 3

Each of the five choices requires a verification of a different property. Unless you are prepared to run each of the 5 tests to choose the option, you could graph the points to help you see which type of triangle it is likely to be, and then do that particular test to confirm.
Graphing three points does not take more than a minute, and is a good investment.

To me it looks like a right triangle.

We will assume that it is a right triangle right angled at E.
In that case, we would have DE perpendicular to EF.

So calculate the slopes of m1=DE and m2=EF, then show that m1*m2=-1.

To calculate slope, use
slope = (y2-y1)/(x2-x1)

Slope of DE, m1= (7-8)/(3-1)=-1/2
Slope of EF, m2 = (8-4)/(1-(-1))=2
So since m1*m2=-1, we conclude that triangle DEF is a right triangle.

Alternatively, use @AlexandervonHumboldt2 's suggestion, and calculate the squares of each side:
DE^2=(7-8)^2+(3-1)^2=5
EF^2=(8-4)^2+(1-(-1))^2=20
FD^2=(7-4)^2+(3-(-1)^2=25

Since DE^2+EF^2=FD^2, the triangle is a right triangle.
We can also see that it is not an isosceles triangle, nor an equilateral triangle, nor acute, nor obtuse (since it is a right triangle).

Answer 4

very detailed explanation @mathmate