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

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Answer 1 · 2018-01-30T08:20:13

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

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)#.