Question

the point a(7,6) is reflected over the point (1,0) and its image is point b. what are the coordinates of point b?

Explanation:

Step1: Use mid - point formula

Let the point of reflection be $P(1,0)$ and the original point be $A(7,6)$ and the image be $B(x,y)$. The mid - point of $AB$ is the point of reflection $P$. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. So, $\frac{7 + x}{2}=1$ and $\frac{6 + y}{2}=0$.

Step2: Solve for $x$

From $\frac{7 + x}{2}=1$, we multiply both sides by 2: $7 + x=2$. Then subtract 7 from both sides: $x=2 - 7=-5$.

Step3: Solve for $y$

From $\frac{6 + y}{2}=0$, we multiply both sides by 2: $6 + y=0$. Then subtract 6 from both sides: $y=-6$.

Answer:

$(-5,-6)$