Answer:
The coordinates of F are (0,6)
Explanation:
We need to compute the slope of the line FE to then use it to find the coordinates of F. To find the slope of the line FE, we use the formula:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (2 - (-5))/(3 - (-5)) = -3/2
Now that we know the slope, we can use point-slope form to find the coordinates of F:
y - y1 = m * (x - x1)
where (x1,y1) is a point on the line or in this case, the point E(-5,2). So we can rewrite the equation as:
y - 2 = (-3/2) * (x + 5)
Moving everything to one side of the equation, we get:
y + 3/2 = (-3/2)x
Divide both sides by (-3/2) and add y1 to both sides, we get:
y / (-3/2) + y1 = x / (-3/2)
y = (-3/2)(x/(-3/2)) + 2
Since we know that y = 6, we can simply plug this value in for y and solve for x:
6 = (-3/2)(x/(-3/2)) + 2
6 = x + 6
x = 0
So the coordinates of F are (0,6), and the equation of the line FE is:
y = (-3/2)x + 6
Therefore, the coordinates of F are:
F = (0,6)
And the equation of the line FE is:
y = (-3/2)x + 6