Question

What is the midpoint of CD?
• (1/2,-5/2)
•(1,-5/2)
•(1/2,-3/2)
•(1,-3/2)

Answer 1

(1/2,-5/2)

Explanation:

`( - 3 + 4 )/(2) = (1)/(2) \\ ( - 4 + - 1)/(2) = ( - 5)/(2)`

Answer 2

`\displaystyle \left((1)/(2),-(5)/(2)\right)`

Explanation:

Given a segment defined by the points (x1,y1) and (x2,y2), the midpoint (xm,ym) is calculated as follows:

`\displaystyle x_m=(x_1+x_2)/(2)`

`\displaystyle y_m=(y_1+y_2)/(2)`

The segment CD is defined by the points in graph C(-3,-4) and D(4,-1). The midpoint is:

`\displaystyle x_m=(-3+4)/(2)=(1)/(2)`

`\displaystyle x_m=(1)/(2)`

`\displaystyle y_m=(-4-1)/(2)=(-5)/(2)`

`\displaystyle y_m=-(5)/(2)`

Thus, the midpoint is:

`\mathbf{\displaystyle \left((1)/(2),-(5)/(2)\right)}`