SOLUTION: The figure shows a triangle ABC with A (1,1), and B (-1,4). The gradients of AB, AC and BC are -3m, 3m and m respectively. a) Find the value of m b) Find the coordinates of C

Question 795704: The figure shows a triangle ABC with A (1,1), and B (-1,4).
The gradients of AB, AC and BC are -3m, 3m and m respectively.
a) Find the value of m
b) Find the coordinates of C
c) Show that AC = 2AB
I have so far attempted question a), in which I got the correct answer:
m = (y2 - y1)/(x2 - x1)
m = 4-1/-1-1 = 3/-2 x 1/-3
m = 1/2
I have attempted question b) but i'm not really sure how to proceed. Let me show what I've tried:
m(BC) = 1/2
y - y1 = m (x - x1)
y - 4 = 1/2 (x+1)
y = 1/2x + 9/2
I'm not sure what to do next.
Please help me! Thank you.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The figure shows a triangle ABC with A (1,1), and B (-1,4).
The gradients of AB, AC and BC are -3m, 3m and m respectively.
a) Find the value of m
b) Find the coordinates of C
c) Show that AC = 2AB
I have so far attempted question a), in which I got the correct answer:
m = (y2 - y1)/(x2 - x1)
m = 4-1/-1-1 = 3/-2 x 1/-3
m = 1/2
I have attempted question b) but i'm not really sure how to proceed. Let me show what I've tried:
m(BC) = 1/2
y - y1 = m (x - x1)
y - 4 = 1/2 (x+1)
y = 1/2x + 9/2 Equation BC
----------
That's the equation of the line thru points B and C.
---
Do the same for AC:
slope = 3m = 3/2
y - y1 = S(x - x1)
y - 1 = 3/2 (x-1)
y = 3x/2 - 1/2 Equation AC
----
Now find the intersection of the lines of the 2 equations, that's point C.
y = 3x/2 - 1/2 Equation AC
y = 1/2x + 9/2 Equation BC
---
y = x/2 + 9/2 = 3x/2 - 1/2
x + 9 = 3x - 1
x = 5
y = 7
Point C is (5,7)
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