Question

triangle ABC has vertices A(–4, 4), B(6, 0), and C(–4, 0). Is triangle ABC a right triangle?
@wolfe8

Answer 1

Calculate lenghts of three sides, do they
Realize Pyhtagoras equation?

Answer 2

whats that?

Answer 3

An easier way is to draw it on a graph paper

Answer 4

i don't have graphing paper, but would my answer be no?

Answer 5

I'll make the graphic

Answer 6

thank you

Answer 7

AC &BC make a right angle?

Answer 8

AC = 4 and BC = 10

If AC² + BC² = BA² then the triangle is a right triangle.
16 + 100 = BA²
116 = BA²
BA = sqrt(116) = 10.7703296143

How do we know what the length of BA is anyway?

Answer 9

so AC &BC do make a right angle, right?

Answer 10

I don't know (it sure looks it)
How can we tell if angle C is a right angle?

Answer 11

because the box in the graph you made, in fits it like a right angle

Answer 12

Yes, but mathematically, how can we prove it is a right angle?
(Just looking like a right angle isn't enough).

Answer 13

how do we prove it?

Answer 14

We have two points at the same y value, no? If we can show that the third point connects to one of those points along a line perpendicular to the line connecting the first two points, we've demonstrated that there is a right angle.

Answer 15

How about calculating Angle B and angle A?
If angle A + angle B = 90° then angle =90°
arc tangent (angle B) = 4/10 = .4
angle B = 21.801°

arc tangent (angle A) = 10/4 = 2.5
angle A = 68.199°

angle A + anngle B = 90°
Therefore angle C = 90°

Answer 16

You can also show that angle C is a right angle directly. AC has undefined slope because the x-values are the same: the equation is x = constant. BC has slope 0 because the y-values are the same: the equation is y = constant. Such a pair of lines is perpendicular because they are parallel to the x and y axes, which are perpendicular.