Question

The point A(4,1) is reflected over the point (0, -3) and its image is point B. Whatare the coordinates of point B?

Answer 1

Step 1: Concept

Given point A (4, 1) reflect over (0, -3). The image is at point B.

Step 2:

Let the coordinate of B = (x,y)

Step 3:

To find image B, apply the formulas below.

$\begin{gathered} 0\text{ = }\frac{\text{x + 4}}{2} \\ \text{Cross multiply} \\ x\text{ + 4 = 2 }\times0 \\ \text{x + 4 = 2} \\ \text{x = -4} \\ \\ -3\text{ = }\frac{y\text{ + 1}}{2} \\ \text{Cross multiply} \\ \text{y + 1 = -3 }\times\text{ 2} \\ y\text{ + 1 = -6} \\ \text{y = -6 - 1} \\ y\text{ = -7} \end{gathered}$

Step 4: Final answer

The coordinates of the image B = (x,y) = (-4,-7)