Question

FG has a midpoint at M(5, 7). Point G is at (9,5). Find the coordinates of point F. Write the coordinates as decimals or integers. ​

Answer 1

i don’t know i need points though

Answer 2

The coordinates of point F are (1, 9), with the midpoint M(5, 7) and point G(9, 5). The midpoint formula was used to determine F's coordinates from M and G.

The midpoint formula is given by:

`\[ M = \left( \frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2} \right) \]`

In this case, the midpoint M is given as
`\( (5, 7) \)` and point G is
`\( (9, 5) \)`. Let F have coordinates (x, y).

Using the midpoint formula:

`\[ 5 = \frac{{x + 9}}{2} \]\[ 7 = \frac{{y + 5}}{2} \]`

Solving these equations will give the coordinates of point F.

1. For the x-coordinate:

`\[ 5 = \frac{{x + 9}}{2} \]\[ 10 = x + 9 \]\[ x = 1 \]`

2. For the y-coordinate:

`\[ 7 = \frac{{y + 5}}{2} \]\[ 14 = y + 5 \]\[ y = 9 \]`

Therefore, the coordinates of point F are
`\( (1, 9) \)`.