Question

Find the midpoint of PQ.

P (3, 5) Q (-2, 13)

Group of answer choices

(1/2, 9)

(4, 9)

(-1/2, 9)

(3, 9)

Answer 1

let mid point of PQ is x,y

then x = 3+(-2)/2

x = 1/2

y = 5+13/2

y = 18/2

y = 9

so the midpoint of PQ is (1/2,9)

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The midpoint of PQ where P (3, 5) Q (-2, 13)

• (1/2, 9)

• (4, 9)

• (-1/2, 9)

• (3, 9)

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$

The midpoint of the line AB is

$\displaystyle \sf{ \bigg( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} \bigg)}$

EVALUATION

Here the given points are P (3, 5) , Q (-2, 13)

Hence the required midpoint of PQ

$\displaystyle \sf{ = \bigg( \frac{3 - 2}{2} , \frac{5 + 13}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{1}{2} , \frac{18}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{1}{2} , 9 \bigg)}$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ \bigg( \frac{1}{2} , 9 \bigg)}$

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