Question

Please I will medal and fan!!!!!!!!!! I am soooo desperate.
The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1).

Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not.

Answer 1

a right triangle is a triangle with one right angle in it

a right angle is a 90 degree angle

2 perpendicular lines will create a 90 degree angle

in order for 2 lines to be perpendicular to each other, their slopes must be negative reciprocals to each other

the slope between two point cans be given as
\[m= \frac{y_2 - y_1}{x_2-x_1}\]

Answer 2

you have 3 points, A, B, C

you can create 3 line segments to create the triangle
AB, BC, AC

what is the slope of AB?
what is the slope of BC?
what is the slope of AC?

Answer 3

Ok I am trying to find the slopes now

Answer 4

1) Slope of AB is =1/2?
2) Slope of BC is 3/4?
3) Slope of AC is 2?

Answer 5

@sooobored

Answer 6

ok they look fine,

are any of the slopes negative reciprocals to each other?

Answer 7

negative reciprocal of a rational number

\[\frac{a}{b} \rightarrow -\frac{b}{a}\]

Answer 8

sorry, slope of AB is wrong

Answer 9

forgot a negative sign in my head

Answer 10

unless that equal sign "=" is suppose to be a negative sign "-"

cause slope of AB should be -1/2

Answer 11

Oh yeah that is supposed to be negative thanks!

Answer 12

well to finish off the question
2 is a negative reciprocal to -1/2

thus the line segment AB and AC just be perpendicular to each other and thus meaning that the triangle is a right triangle since one of its sides is a right angle/90 degrees/ perpendicular