Question

find the midpoint of the segment having the given endpoints. (6,9) and (1,4)

a. (\frac{13}{2},\frac{7}{2})
b. (7,13)
c. (\frac{7}{2},\frac{13}{2})
d. (5,5)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify the values of $x_1,y_1,x_2,y_2$

Here $x_1 = 6,y_1=9,x_2 = 1,y_2 = 4$.

Step3: Calculate the x - coordinate of the mid - point

$\frac{x_1+x_2}{2}=\frac{6 + 1}{2}=\frac{7}{2}$.

Step4: Calculate the y - coordinate of the mid - point

$\frac{y_1+y_2}{2}=\frac{9+4}{2}=\frac{13}{2}$.

Answer:

C. $(\frac{7}{2},\frac{13}{2})$