Question

The coordinates of the endpoints of EF are E( – 9,11) and F(1,6). Point G is on EF and divides it such that EG:FG is 2:3. What are the coordinates of G?

Answer 1

To find the coordinates of point G on the line segment EF, we can use the formula for dividing a line segment in a given ratio. The coordinates of point G are (-5, 9).

Step-by-step explanation:

To find the coordinates of point G on the line segment EF, we need to find the point that divides EF in a ratio of 2:3. Here's how we can do that:

Calculate the difference in x-coordinates: 1 - (-9) = 10

Calculate the difference in y-coordinates: 6 - 11 = -5

Multiply the difference in x-coordinates by 2/5 and add it to the x-coordinate of E: (-9) + (10 * 2/5) = -9 + 4 = -5

Multiply the difference in y-coordinates by 2/5 and add it to the y-coordinate of E: 11 + (-5 * 2/5) = 11 - 2 = 9

The coordinates of point G on the line segment EF are (-5, 9).