Question

A triangle given by a (2, 2), b (5, 2), c (5, 5), is to be reflected about an arbitrary point
(x, y). The new positions are given by (12, 8), (9, 8), (9, 5). Determine the values of x and y.

Information about the question’s affiliation :-
Dep. of Production Engineering and Metallurgy
subject : Computer aided design and manufacturing

Answer 1

Point of Reflection is same as the mid-point of line joining the vertices and corresponding reflected vertices.

Mid-point of a=(2,2) and (12,8) is $\small \left ( \frac{2+12}{2},\frac{2+8}{2} \right )=\left ( 7,5 \right )$

Similiarty for b=(5,2) and (9,8) is $\small \left ( \frac{5+9}{2},\frac{2+8}{2} \right )=\left ( 7,5 \right )$

Finally for c=(5,5) and (9,5) is

5 +9 5 + 5 2 ง + = (7, 5)

The values of x and y are 7 and 5 respectively. I hope this helps. Please do rate me and let me know if you have any query.