Question

The coordinates of the endpoints of FG are F(-8, 3) and G(-2, -9). Point H is on FG and

divides it such that FH:GH is 1:2.
What are the coordinates of H?
Write your answers as integers or decimals.

Answer 1

To find the coordinates of point H on line FG, we divide the line segment FG into two parts in the ratio 1:2. The x-coordinate of H is obtained by dividing the difference in x-coordinates of F and G by 3, and the y-coordinate is obtained by dividing the difference in y-coordinates of F and G by 3. The coordinates of H are (-2, 4).

Step-by-step explanation:

To find the coordinates of point H, we need to divide the line segment FG into two parts, such that FH:GH is 1:2.

We can start by finding the x-coordinate of point H. The x-coordinate of F is -8 and the x-coordinate of G is -2. Since FH:GH is 1:2, the difference in x-coordinates for FH and GH will also be in the ratio 1:2. So, we can find the x-coordinate of H by dividing the difference in x-coordinates of F and G by 1+2 = 3.

The difference in x-coordinates of F and G is -8 - (-2) = -6. When we divide this by 3, we get -2. Therefore, the x-coordinate of H is -2.

Next, we can find the y-coordinate of H. The y-coordinate of F is 3 and the y-coordinate of G is -9. We can follow the same process as above. The difference in y-coordinates of F and G is 3 - (-9) = 12. When we divide this by 3, we get 4. Therefore, the y-coordinate of H is 4.

Therefore, the coordinates of point H are (-2, 4).

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