If ΔOPQ is dilated from point Q by a scale factor of 3, which of the following equations is true about segment R prime S prime? 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.

segment R prime S prime = one half segment RS
segment R prime S prime = two segment RS
segment R prime S prime = segment RS
segment R prime S prime = three segment RS

Given:

ΔOPQ is dilated from point Q by a scale factor of 3.

To find:

The correct equation about segment R'S'.

Solution:

In triangle OPQ, point R lying on side OP and point S lying on side OQ.

Line RS is perpendicular to side OQ.

In dilation, we either compress or enlarge the figure according to the scale factor. It means, the preimage and image are similar figure.

We know that, corresponding sides of similar figures are proportional and equal to the scale factor.

ΔOPQ is dilated from point Q by a scale factor of 3.

RS and R'S' are corresponding sides and scale factor is 3. So,

Therefore, the correct option is D.

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d