We want to find the equation of a line that is perpendicular to G and pass through point (P, Q)
The coordinate of G is
(-2,6) and (-3,2)
Point 1 = (x1,y1) = (-2,6)
Point 2 = (x2,y2) = (-3,2)
So, let find the slope of this line G.
Slope can be calculated using
m = ∆y/∆x
m = (y2 - y1) / (x2 - x1)
m = (2-6) / (-3--2), -×- = +
m = -4 / (-3 + 2)
m = -4 / -1
m = 4
So, the gradient or slope of line G is 4
From geometry, since the equation of the line we want to find is perpendicular to the G,
Then, the slope of the line is
m2 = -1 / m1
m2 = - 1 / 4
m2 = -¼.
Then, also we can write equation of a line given the slope and a point using
m = (y - y1) / (x - x1)
Where m = -¼
And the point (x1,y1) = (P, Q)
Then, we have
-¼ = (y - Q) / (x - P)
Cross multiply
-(x - P) = 4(y - Q)
-x + P = 4y - 4Q
Rearrange
-x - 4y = - 4Q - P
Divide through by -1
x + 4y = 4Q + P
Then, the last option is correct
