Question

Please help can't decide which one it is. I have it graphed but I can't tell what it is. WILL MEDAL!!! @phi

Answer 1

this looks painful
I would first plot the points just to see what it looks like

Answer 2

Here is a plot from geogebra

Answer 3

by eyeball it looks like it could be a right triangle.
To prove it, we would find the slopes from A to B
and the slope from B to C

can you do that ?

Answer 4

find the slope between (1,4) and (3,1)
change in y divided by change in x

Answer 5

I would do the y value from (1,4) minus the y value from (3,1)
can you do that ?

Answer 6

now do the x value of (1,4) minus the x value from (3,1)

Answer 7

now the slope is 3/-2 or -3/2

next we find the slope from B to C
(3,1) and (6,3)
can you do that ?

Answer 8

first "change in y"

Answer 9

and the slope is ⅔ (the minus/minus becomes plus)

Answer 10

if the slopes of two lines are "negative reciprocals" that means the lines form a right angle
negative reciprocal means if one has slope m, the other has slope -1/m

or , (means the same thing)
if you multiply the two slopes, you get -1

Answer 11

in this case
\[ - \frac{3}{2} \cdot \frac{2}{3}= -1 \]
proves the lines AB and BC form a 90 degree angle, so the triangle ABC is a right triangle (because it has a 90 degree angle in it)

Answer 12

notice I used the graph to guess which lines to check. If we did not have the picture, we would have to check all 3 angles... lots of work