Question

Find all values of k so that (-1,2), (-10,5), and (-4,k) are the vertices of a right triangle.

Answer 1

use length formula to find the length of the first two sides and then use pythagorean theorem to finf the length of the last side and substitute the known values and find k

Answer 2

Thanks @MohamedDada

Answer 3

i try =D

Answer 4

what's the length formula ?

Answer 5

Its sqrt((x1-x2)^2+(y1-y2)^2) anyway do you know slope formula that a better formula to use in this question...

Answer 6

d = (sqrt(x2 - x1)^2 (y2-y1)^2)

Answer 7

can you do the first steps for me? I'm seriously confused, geometry is to hard for me :[

Answer 8

msn?

Answer 9

i don't have msn

Answer 10

ok ill just do it here

Answer 11

okay [:

Answer 12

\[d = \sqrt{(-10 + 1) (5 - 2)}\]

Answer 13

wait

Answer 14

Err that is not correct it is sqrt(9^2+3^2)=sqrt(90).

Answer 15

i know -.-

Answer 16

lol thanks

Answer 17

which one iisnt rght ?

Answer 18

i forgot to square

Answer 19

Ok i'll tell you how to do it THe product of slope's of the lines which are perpendicular are -1 so slopes of the three lines are
1. (k-5)/6
2. 3/-9=-1/3
3. (k-2)/(-3)=(2-k)/3
So you take them in pairs and apply the given conditon that product is -1.
I'll do one for you i'll take 1 and 3 and mutiply equating to -1,
(k-5)(2-k)/(6*3)=-1, k^2-7k+-8=0
(k-8)(k+1)=0 k=8,k=-1. These are two values now you take the remaining two pairs and do it you'll get two more vaules.

Answer 20

Do you know slope formula?

Answer 21

i'm not sure
is this all the steps? o.o

Answer 22

Slope formula slope of a line is (y2-y1)/(x2-x1)
So the first slope is(k-5)(-4-(-10)) you get (k-5)/6.

Answer 23

oh okay

Answer 24

how did you get the (-8) ??? i did it several times and i get -9 !!!