Question

EFG is a straight line and the length of EF is equal to the length of FG. Point F has coordinates (11,24). Point G has coordinates (4,27). What are the coordinates of point E ?

Answer 1

The coordinates of point E are (18 , 21).

As F is the midpoint of line EFG, we can use the midpoint formula to solve for the coordinates of E.

Given:

Point F has coordinates (11, 24).

Point G has coordinates (4, 27).

The midpoint formula states that the midpoint F between points E and G is:

`\[F = \left((x_E + x_G)/(2), (y_E + y_G)/(2)\right)\]`

And we're given that F is (11, 24).

Now, substituting the coordinates of F and G:

`\[(x_E + 4)/(2) = 11 \implies x_E + 4 = 22 \implies x_E = 22 - 4 = 18\]`

`\[(y_E + 27)/(2) = 24 \implies y_E + 27 = 48 \implies y_E = 48 - 27 = 21\]`

Therefore, using the midpoint formula and the given information, the coordinates of point E are (18, 21), confirming the solution provided earlier.

Answer 2

Applying the midpoint formula, the coordinates of point E are determined as: (18, 21).

What is the midpoint formula?

The midpoint formula is a mathematical expression,
`\((x_1 + x_2)/(2), (y_1 + y_2)/(2)\)`, used to find the coordinates of the midpoint between two points. In this case, F is the midpoint which is (11, 24). Therefore:

F(x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Where:

x = 11

y = 24

E(?, ?) = (x₁, y₁)

G(x₂, y₂) = (4, 27)

Plug in the values:

F(11, 24) = [(x₁ + 4)/2, (y₁ + 27)/2]

Solve each coordinates separately:

11 = (x₁ + 4)/2

22 = x₁ + 4

22 - 4 = x₁

x₁ = 18

24 = (y₁ + 27)/2

48 = y₁ + 27

48 - 27 = y₁

y₁ = 21

Therefore, the coordinates of point E are: (18, 21).