Answer:
(3, 6)
1/3
y = -3x +15
Explanation:
you do this step by step.
just think what you need. and then you get all of that one after the other.
so, we need the middle point between D and O.
for this we need to know the length of DO.
and we need the slope of DO, so that we can then calculate the perpendicular slope. with that slope we then build the line going through the middle point as well but with the perpendicular slope.
so, length of DO.
Pythagoras for the triangle of the differences between the individual coordinates.
DO² = (9- -3)² + (8-4)² = (9+3)² + 4² = 144 + 16 = 160
DO = sqrt(16×10) = 4×sqrt(10)
the distance D-middle is half of DO = 2×sqrt(10)
DO/2 => DO²/4 = 144/4 + 16/4 = 36 + 4 = 6² + 2²
=> we have to add to the coordinates of D 6 in x and 2 in y direction to get the middle point :
(-3 + 6, 4 + 2) = (3, 6)
the slope of DO
the slope of a line is the ratio of y/x representing the change of y with the change of x. it is the factor of x in the line equation.
for DO we know that when x changes by 12 (difference of the x values of D and O), then y changes by 4.
so, the slope is 4/12 = 1/3.
perpendicular slope of 1/3
we flip x and y and also change the sign, as when the original line goes up, then the y line goes down. and vice versa.
so, the perpendicular slope is -3/1 = -3
the equation of the perpendicular line through the middle point is
y = -3x + c
for c we need to use the coordinates of the middle point (3, 6)
6 = -3×3 + c
6 = -9 + c
c = 15
so our line is
y = -3x + 15