On a coordinate grid, a line segment connects the points A(1, 3) and B(9, 15). The midpoin… — ACT

On a coordinate grid, a line segment connects the points $A(1, 3)$ and $B(9, 15)$ . The midpoint of this segment is $M$ , and the midpoint of the segment connecting $A$ and $M$ is $C$ . What is the $y$ -coordinate of point $C$ ?

Answer: 6

Answer

The

y

-coordinate of point

C

is 6.

Applying the midpoint formula to the endpoints

A(1, 3)

and

B(9, 15)

yields

M(5, 9)

. Applying the midpoint formula again to

A(1, 3)

and

M(5, 9)

yields

C(3, 6)

. The

y

-coordinate of point

C

is therefore 6.

Step-by-Step Solution

Calculate the coordinates of the midpoint

M

of segment

AB

M = (5, 9)

The midpoint formula is defined as

\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Calculate the coordinates of the midpoint

C

of segment

AM

C = (3, 6)

Apply the midpoint formula using the coordinates of

A(1, 3)

and the newly found midpoint

M(5, 9)

Identify the

y

-coordinate of point

C

For the point

C(3, 6)

, the

x

-coordinate is 3 and the

y

-coordinate is 6.

Key Concept

Midpoint Formula

Estimated Time:1m 15s

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