We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

The points $B(1, 1)$, $I(2, 4)$ and $G(5, 1)$ are plotted in the standard rectangular coordinate system to form triangle $BIG$. Triangle $BIG$ is translated five units to the left and two units upward to triangle $B'I'G'$, in such a way that $B'$ is the image of $B$, $I'$ is the image of $I$, and $G'$ is the image of $G$. What is the midpoint of segment $B'G'$? Express your answer as an ordered pair.

Guest Jun 19, 2018

#1**0 **

The STARTING midpoint of BG is at 3, 1 then it is translated 5 to the left

so the 'x' coordinate becomes 3-5 = -2

and translated UP 2 units

so the 'y' coordinate becomes 1+2 = 3

(-2,3)

ElectricPavlov Jun 19, 2018

#2**0 **

**The points $B(1, 1)$, $I(2, 4)$ and $G(5, 1)$ are plotted in the standard rectangular coordinate system to form triangle $BIG$. **

**Triangle $BIG$ is translated five units to the left and two units upward to triangle $B'I'G'$, **

**in such a way that $B'$ is the image of $B$, $I'$ is the image of $I$, and $G'$ is the image of $G$. **

**What is the midpoint of segment $B'G'$? **

**Express your answer as an ordered pair.**

\(\begin{array}{|l|lrr|} \hline & \text{translation} \\ & x' =x-5\\ & y' = y +2 & \\ \hline \text{B} =(1,1) & \text{B'} =(1-5,1+2) = (-4,3) \\ \text{I} = (2,4) & \text{I'} = (2-5,4+2) = (-3,6) \\ \text{G} = (5,1) & \text{G'} = (5-5,1+2) = (0,3) \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline \text{midpoint of } B'G' &=& \dfrac{B'+G'}{2} \\\\ &=& \dfrac{\dbinom{-4}{3}+\dbinom{0}{3}}{2} \\\\ &=& \dfrac{\dbinom{-4+0}{3+3}}{2} \\\\ &=& \dfrac{\dbinom{-4}{6}}{2} \\\\ &\mathbf{=}& \mathbf{ \dbinom{-2}{3} } \\ \hline \end{array}\)

heureka Jun 20, 2018