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38:Ta48,

Find the midpoint of the line segment joining $(2,4)$ and $(8,10)$.

$(3,3)$

$(5,7)$

$(6,6)$

$(10,14)$

Average the $x$-coordinates and the $y$-coordinates: $\left(\frac{2+8}{2},\frac{4+10}{2}\right)=(5,7)$.

What is the midpoint of the line segment joining $(-6,3)$ and $(4,11)$?

$(-2,8)$

$(1,7)$

$(-5,4)$

$(-1,7)$

The midpoint is $\left(\frac{-6+4}{2},\frac{3+11}{2}\right)=\left(\frac{-2}{2},\frac{14}{2}\right)=(-1,7)$.

Find the midpoint of the line segment joining $(1.5,-2)$ and $(4.5,6)$.

$(3,2)$

$(3,4)$

$(2,3)$

$(6,4)$

Average each pair of coordinates: $\frac{1.5+4.5}{2}=3$ and $\frac{-2+6}{2}=2$, so the midpoint is $(3,2)$.

One endpoint of a line segment is $(1,-3)$ and its midpoint is $(4,1)$. What is the other endpoint?

$(2,-1)$

$(5,4)$

$(7,5)$

$(8,2)$

From $(1,-3)$ to the midpoint $(4,1)$, the change is $(+3,+4)$. Make the same change again to get the other endpoint: $(4+3,1+4)=(7,5)$.

The midpoint of the line segment joining $(2,y)$ and $(8,12)$ is $(5,9)$. Find $y$.

$3$

$6$

$7$

$10$

The midpoint's $y$-coordinate is the average, so $\frac{y+12}{2}=9$. Therefore $y+12=18$, giving $y=6$.

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