Answer:
The equation of the line perpendicular to AC and passing through point B is y = -x + 4
Step-by-step explanation:
We start by finding the slope and equation of line AC
The equation of a straight line can be given as;
y = mx + c
where m is the slope and c is the y-intercept
Mathematically, the slope is given as;
m = (y2-y1)/(x2-x1)
m = (7-2)/(2-(-3)) = 5/5 = 1
So the equation becomes ;
y = x + c
We only need the slope since we are trying to get another line perpendicular to this
If two lines are perpendicular, then the product of the slopes of both lines is equal to -1
This means that m1 * m2 = -1
So this means that the slope of the perpendicular line is -1/1 = -1
Thus, the equation of the line we are finding would be;
y = -x + c
since it passes through line B, we can make a substitution of the coordinates of point B
That would be;
7 = -(-3) + c
7 = 3 + c
c = 7-3
c = 4
So the equation of that line is;
y = -x + 4 or simply y = 4-x
