MATH SOLVE

4 months ago

Q:
# 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)

(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)