Question

On a coordinate plane, a line F G goes through (negative 8, negative 8) and (8, 4). Point H is at (6, negative 6).

Which point is on the line that passes through point H and is perpendicular to line FG?

(–6, 10)
(–2, –12)
(0, –2)
(4, 2)

Answer 1

To find the point on the line that is perpendicular to line FG and passes through point H, we need to find the equation of line FG and then find the point of intersection. The equation of line FG is y = (3/4)x - 10 and the equation of the line perpendicular to FG passing through H is y = (-4/3)x - 2. The point of intersection is (6, -8).

Step-by-step explanation:

To find a point on the line that passes through point H and is perpendicular to line FG, we first need to find the equation of the line FG. We can do this by finding the slope of line FG using the formula (y2 - y1)/(x2 - x1). The slope of line FG is (4 - (-8))/(8 - (-8)) = 12/16 = 3/4.

Since the line we're looking for is perpendicular to line FG, its slope will be the negative reciprocal of 3/4, which is -4/3. Using the slope-intercept form of a line, y = mx + b, we can substitute the known coordinates of point H and the slope of the line (-4/3) to find the y-intercept, b. The equation of the line is y = (-4/3)x + (-2).

Substituting the x-coordinate of point H, which is 6, we can find the y-coordinate of the point on the line that passes through point H and is perpendicular to line FG. y = (-4/3)(6) + (-2) = -8.

Therefore, the point on the line that passes through point H and is perpendicular to line FG is (6, -8).

Answer 2

(–6, 10)

Step-by-step explanation:

Because the line is perpendicular its slope is the negative reciprocal of line FG. If we examine the graph and plot out the slope we see that it crosses point (–6, 10).