Question

A pool company is creating a blueprint for a family pool and a similar dog pool for a new client. Which statement explains how the company can determine whether pool LMNO is similar to pool PQRS?

Translate PQRS so that point P of PQRS lies on point L of LMNO, then dilate PQRS by the ratio segment LM over segment PQ.



Translate PQRS so that point Q of PQRS lies on point M of LMNO, then dilate PQRS by the ratio segment PQ over segment LM.



Translate PQRS so that point P of PQRS lies on point L of LMNO, then translate PQRS so that point Q of PQRS lies on point M of LMNO.



Translate PQRS so that point Q of PQRS lies on point M of LMNO, then translate PQRS so that point P of PQRS lies on point L of LMNO.

Answer 1

To verify the similarity between the two pools, translate pool PQRS so that point P coincides with point L of pool LMNO, then perform a dilation using the ratio of LM over PQ. If both pools coincide after the dilation, they are similar. Option 'A'.

Step-by-step explanation:

To determine whether two shapes like pool LMNO and pool PQRS are similar, the company would need to ensure that the shapes are geometrically the same in shape but not necessarily in size, which means corresponding angles are equal and corresponding sides are proportional. The translation and dilation processes are methods of moving and resizing shapes to verify this similarity.

In this case, the correct transformation sequence would be to translate PQRS so that point P of PQRS lies on point L of LMNO. Following the translation, the next step should be to dilate PQRS by the ratio of segment LM over segment PQ. If PQRS can be dilated to coincide exactly with LMNO, then the pools are geometrically similar, which means that their corresponding angles are equal, and their sides are in proportional lengths.