Question

Grace has a segment with endpoints F (4, 9) and G (7, 2) that is divided by a point H such that FH and GH form a 1:3 ratio. She knows that the distance between the x coordinates is 3 units. Which of the following fractions will let her find the x coordinate for point H?

Answer 1

To find the x-coordinate for point H on a line segment divided in a 1:3 ratio, use the section formula to calculate it as 4.75, which is the weighted average of the x-coordinates of endpoints F and G.

Step-by-step explanation:

To find the x-coordinate for point H on the segment with endpoints F (4, 9) and G (7, 2) with a ratio of FH to GH as 1:3, we need to use the concept of section formula in coordinate geometry. Since we are given that the distance between the x-coordinates of F and G is 3 units, we can infer that the overall segment has been split into 4 equal parts because of the 1:3 ratio between FH and GH. The x-coordinate of H thus divides the segment such that H is 1 part from F and 3 parts from G.

We then use the section formula to find the x-coordinate of H, which is ((1*7) + (3*4)) / (1+3) = (7 + 12) / 4 = 19 / 4 = 4.75. Therefore, the x-coordinate for point H is 4.75.

Following the steps above will lead Grace to the correct calculation of the x-coordinate of point H, and she can apply the same process for finding the y-coordinate if needed.