Question

Point H lies on FG, where F is located at (-3.5,-11) and G is located at (4.5,-5). The ratio of FH to GH is 1:3. What is the sum of the coordinates of H ? Write your answer as an integer or decimal.

Answer 1

To find the coordinates of point H on the line segment FG, we use the ratio 1:3. By calculating the differences in x and y coordinates between points F and G and multiplying them by the ratio, we can determine the coordinates of point H. The sum of the coordinates of H is -11.

Step-by-step explanation:

To find the coordinates of point H, we need to determine the point that divides the segment FG into a 1:3 ratio.

First, we calculate the difference in x-coordinates and the difference in y-coordinates between points F and G:
Δx = 4.5 - (-3.5) = 8
Δy = (-5) - (-11) = 6

Next, we find the coordinates of point H by multiplying both Δx and Δy by the ratio 1:3 and adding the results to the coordinates of point F:
x-coordinate of H = -3.5 + (1/4) * 8 = -1.5
y-coordinate of H = -11 + (1/4) * 6 = -9.5

The sum of the coordinates of point H is -1.5 + (-9.5) = -11.