Question

Segment FB is graphed on the coordinate plane where F is negative seven, negative four and B is (5,2). If point A is graphed

of the way from F to B, where is point A located?

Answer 1

To find the coordinates of point A, which is one-fourth of the way from point F to B on the coordinate plane, calculate one-fourth of the distance between F and B's x and y coordinates and add them to F's coordinates. The resulting location of point A is (-4, -2.5).

Step-by-step explanation:

The student is asking about finding a point on a line segment on the coordinate plane that is one-fourth of the way from point F to point B. To find the location of point A, which is one-fourth of the way from F to B, we first need to find the distances between the x-coordinates and the y-coordinates of points F and B.

Let's denote the coordinates of F as (Fx, Fy) = (-7, -4) and the coordinates of B as (Bx, By) = (5, 2). The differences in coordinates are:

• x-coordinate difference: Bx - Fx = 5 - (-7) = 12
• y-coordinate difference: By - Fy = 2 - (-4) = 6

To find the coordinates of A located one-fourth of the way from F towards B, we calculate one-fourth of these distances and add the result to the coordinates of F:

• Ax = Fx + 1/4 * (Bx - Fx)
• Ay = Fy + 1/4 * (By - Fy)

Therefore:

• Ax = -7 + 1/4 * 12 = -7 + 3 = -4
• Ay = -4 + 1/4 * 6 = -4 + 1.5 = -2.5

So the coordinates of point A are (-4, -2.5).