Line A passes through the points (-4,-11) and (2,13) Line B passes through the points (3,-1) and (-5,31) where does line A intersect line B?
Accepted Solution
A:
First, you need to calculate the equations of line A and line B
(1) Line A:
First let's calculate the gradient: m = (y2-y1)/(x2-x1) = (13-(-11))/(2-(-4)) = 24/6 = 4
Now we can use one of the points, let's take (2,13), and the gradient and substitute these into the equation: y - y1 = m(x - x1) y - 13 = 4(x - 2) y = 4x - 8 + 13 y = 4x + 5
(2) Line B
m = (31-(-1))/(-5-3) = 32/-8 = -4
Taking the point (3,-1): y - (-1) = -4(x - 3) y = -4x + 12 - 1 y = -4x + 11
Now we can equate the two equations to see where they intersect:
4x + 5 = -4x + 11 8x = 6 x = 3/4
Now substitute the value of x into one of the equations:
If x = 3/4: y = -4(3/4) + 11 = -3 + 11 = 8
Therefor Line A intersects Line B at the point (3/4, 8)