Question

PLEASE HELP ASAP!!!

What is the midpoint of AC?

A. (4a, 4b)
B. (2a, 2b)
C. (a, b)
D. (a/2, b/2)

Answer 1

Choice C is correct.

Explanation:

The formula to find mid-point of a line segment is:

M= (
`x_(1)+x_(2)`/2,
`y_(1) +y_(2)`/2)

where (
`x_(1) ,y_(1)`) and (
`x_(2) ,y_(2)`) are end-points of a line segment.

we have to find mid-point of AC.

A is located at the center of xy-graph.

hence, A(
`x_(1) ,y_(1)`) is given as (0,0) and C(
`x_(2) ,y_(2)`) is given as (2a,2b).

put above values in the formula of mid-point formula:

M=(0+2a/2,0+2b)

M=(2a/2,2b/2)

M=(a,b) is mid-point of AC.

Answer 2

C. (a, b)

Explanation:

The formula of a midpoint:

`M\left((x_1+x_2)/(2);\ (y_1+y_2)/(2)\right)`

We have A(0, 0) and C(2a, 2b). Substitute:

`x=(0+2a)/(2)=(2a)/(2)=a\\\\y=(2b+0)/(2)=(2b)/(2)=b`

M(a, b)