Answer:
Gradient of Line ⊥ to AB = m = 3
B) y = 3x+11
Step-by-step explanation:
A) Firstly, finding the slope of AB
Gradient = [tex]\frac{rise}{run}[/tex]
Gradient = [tex]\frac{y2-y1}{x2-x1}[/tex]
Gradient = [tex]\frac{-2-2}{7+5}[/tex]
Gradient = [tex]\frac{-4}{12}[/tex]
Gradient = [tex]\frac{-1}{3}[/tex]
Now, the line has a gradient of negative reciprocal to this one which is perpendicular to AB
So,
Gradient of Line ⊥ to AB = m = 3
B) Equation of line ⊥ to AB:
Gradient = m = 3
Now, Point = (x,y) = (-2,5)
So, x = -2, y = 5
Putting this in slope-intercept form to get b
=> [tex]y = mx+b[/tex]
=> 5 = (3)(-2) + b
=> 5+6 = b
=> b = 11
Now, Putting m and b in the slope intercept form to get the required equation:
=> [tex]y = mx+b[/tex]
=> y = 3x+11
