Question

With the ratio at 1:1, Point C appears to be the midpoint. Use the midpoint formula to ascertain (make sure of) whether Point C is at the midpoint. Explain how the ratio 1:1 would place Point C at the midpoint of AB.

Answer 1

See Explanation

Explanation:

The question is incomplete because the coordinates of A, B and C were not given in the question.

However, the following explanation will guide you...

The midpoints, C of two point A and B is calculated as:

`C(x,y) = ((x_1 + y_1)/(2), (y_1 + y_2)/(2))`

Where
`(x_1, y_1)` are the coordinates of A

and

`(x_2,y_2)` are the coordinates of B

Take for instance, the given coordinates are

A(4,6); B(2,4) and C(3,5)

Then;

Plug in these values in the given formula:

`C(x,y) = ((x_1 + y_1)/(2), (y_1 + y_2)/(2))`

`(3,5) = ((4 + 2)/(2), (6 + 4)/(2))`

`(3,5) = ((6)/(2), (10)/(2))`

`(3,5) = (3,5)`

In that case,

C is really the midpoint

To the b part: Explaining why ratio 1:1 is used

The reason is that both parts of the ratio are in equal proportion (1 and 1);

Because of this equal proportion, ration 1:1 is right to calculate the midpoint