Question

o is the midpoint of yz. the coordinates of y are (4, 6) and the coordinates of o are (2, 5). find the coordinates of z.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of $Y=(x_Y,y_Y)=(4,6)$ and the coordinates of $O=(x_O,y_O)=(2,5)$, and the coordinates of $Z=(x_Z,y_Z)$. Then $x_O=\frac{x_Y + x_Z}{2}$ and $y_O=\frac{y_Y + y_Z}{2}$.

Step2: Solve for $x_Z$

We know that $x_O = 2$ and $x_Y=4$. Substitute into $x_O=\frac{x_Y + x_Z}{2}$, we get $2=\frac{4 + x_Z}{2}$. Multiply both sides by 2: $2\times2=4 + x_Z$, so $4 = 4+x_Z$. Then $x_Z=0$.

Step3: Solve for $y_Z$

We know that $y_O = 5$ and $y_Y = 6$. Substitute into $y_O=\frac{y_Y + y_Z}{2}$, we get $5=\frac{6 + y_Z}{2}$. Multiply both sides by 2: $5\times2=6 + y_Z$, so $10=6 + y_Z$. Subtract 6 from both sides: $y_Z = 4$.

Answer:

$(0,4)$