Question

Can somebody please help me with this question i attached the photo from khan academy.

Answer 1

Answer:

C = (12, 13)

Step-by-step explanation:

The centre of the rectangle is O.

Find the difference between the x and y-values of O and A:

$O_x-A_x=\dfrac{21}{2}-9=\dfrac32$

$O_y-A_y=\dfrac{19}{2}-6=\dfrac72$

Now add those difference to the coordinates of O to find C:

x value of C = $O_x+\dfrac32=\dfrac{21}{2}+\dfrac32=\dfrac{24}{2}=12$

y value of C = $O_y+\dfrac72=\dfrac{19}{2}+\dfrac72=\dfrac{26}{2}=13$

Therefore, the coordinates of C = (12, 13)

Answer 2

Answer:

Step-by-step explanation:

In rectangle the diagonals bisect each other. So,O is the midpoint of AC

$Midpoint = \left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2} \right)\\\\\\x_{1}=9 \ and \ y_{1}=6\\\\\left(\dfrac{9+x_{2}}{2},\dfrac{6+y_{2}}{2} \right) = \left (\dfrac{21}{2},\dfrac{19}{2} \right)$

Compare the x- coordinates and y- coordinates

$\dfrac{9+x_{2}}{2}=\dfrac{21}{2} \ ; \ \dfrac{6+y_{2}}{2}=\dfrac{19}{2}\\\\\\9+x_{2}=\dfrac{21}{2}*2 \ ; \ 6 +y_{2}=\dfrac{19}{2}*2$

9 + x₂ = 21         ;  6 +y₂ = 19

     x₂ = 21 -9     ;       y₂ = 19 - 6

     x₂ = 12         ;        y₂ = 13

C(12 ,13)