Question

question the point a(-2, 3) is reflected over the point (1, 0) and its image is point b. what are the coordinates of point b? answer attempt 1 out of 2

Explanation:

Step1: Recall the mid - point formula

The mid - point of two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. If point $A(x_1,y_1)=(-2,3)$ is reflected over point $M(1,0)$ to get point $B(x_2,y_2)$, then the mid - point of $A$ and $B$ is the point of reflection. So, $\frac{x_1 + x_2}{2}=1$ and $\frac{y_1 + y_2}{2}=0$.

Step2: Solve for the $x$ - coordinate of $B$

We have $\frac{-2 + x_2}{2}=1$. Multiply both sides by 2: $-2+x_2 = 2$. Add 2 to both sides: $x_2=4$.

Step3: Solve for the $y$ - coordinate of $B$

We have $\frac{3 + y_2}{2}=0$. Multiply both sides by 2: $3 + y_2=0$. Subtract 3 from both sides: $y_2=-3$.

Answer:

$(4,-3)$