How to find the value of m and the coordinates of C?

enter image source here enter image source here

1 Answer
Jan 30, 2018

m=1/2, and, C=C(5,7).

Explanation:

Supoose that, C=C(a,b).

Given that, A=A(1,1), and B=B(-1,4).

Let us denote, by Grad(AB), the gradient of AB.

Then, Grad(AB)=(4-1)/(-1-1)=-3/2=-3m........."[Given]".

:. m=1/2...........................................................................(1).

"Given that "Grad(AC)=3m, &, (1) rArr (b-1)/(a-1)=3/2,

:. 2b-2=3a-3, or, 3a-2b=1...............................(2).

Likewise, Grad(BC)=m, &, (1)rArr(b-4)/(a-(-1))=(b-4)/(a+1)=1/2,

:. 2b-8=a+1, i.e., 2b-a=9....................................(3).

(2)+(3) rArr 2a=10 rArr a=5

a=5, and, (3) rArr b=7.

Thus, m=1/2, and, C=C(a,b)=C(5,7).