It's !
triangle opq is shown below with line rs passing through points r and s:

triangle opq is shown with point r lying on side op and point s lying on side oq line rs is perpendicular to side oq.

if triangle opq is dilated about the center of the triangle to create triangle o'p'q', what can you conclude about segments rs and r's'?

segment o'q' is perpendicular to segment r's'.
line rs is parallel to line r's'.
line rs is perpendicular to line r's'.
point p' passes through line rs.

Segment O'Q' is perpendicular to segment R'S'  

Line RS is parallel to line R'S'

Step-by-step explanation:

Dilation about a point does not change the relations among the various segments. It makes a object larger or smaller.  

The diagram below shows a dilation of ∆OPQ into ∆O'P'Q'.

We can see that

C is wrong, because RS∥RS'.

D is wrong, because P' does not pass through RS

A.) Segment O'Q' is perpendicular to segment R'S'.

IS WRONG!!

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq