gradient, equation of a line and finding coordinates?

Question

The line AC is perpendicular to the line AB.

1) find the gradient of AC
2)find the equation of line AC
3) given that point c lies on the x-axis find its x coordinate

Line AB HAS EQUATION 3X +4Y =7
A coordinates (1,1)
B coordinates (5,-2)
and midpoint (3,-0.5)

Answer 1

AB can be written y = -3/4x + 7/4

slope = -3/4

slope of AC is 4/3

y = 4/3 x + c or 3y = 4x + 3c insert (1,1)

3y = 4x -1

when y = 0, x = 1/4

Answer 2

Rearrange the equation to the form y=bx +c: 5y = -3x + 12, y = -3/5x + 12/5 Then the gradient is the extensive sort in front of the "x" - ie that is -3/5 to locate the place it crosses the axis, you opt for to locate the place x = 0 and the place y = 0. So, purely replace those values into the equation. y = -3/5(0) + 12/5 as a result y = 12/5. to locate x, 0 = -3/5x + 12/5. 3/5x = 12/5 x = 12/5 divided with the aid of 3/5. i think like i've got purely completed your homework. perhaps you need to ask your instructor to describe it because of the fact that could be a notably uncomplicated question to get caught on.

Answer 3

1) find the gradient of AC = 4/3

2)find the equation of line AC
=> y- 1 = 4/3 ( x -1 )
etc

3) given that point c lies on the x-axis find its x coordinate
=> Let y = 0 in
y- 1 = 4/3 ( x -1 ) & find x
etc