Question

a square with side lengths of 3 cm is reflected vertically over a horizontal line of reflection that is 2 cm below the bottom edge of the square. what is the distance between the points c and c’? \\(\boldsymbol{\square}\\) cm what is the perpendicular distance between the point b and the line of reflection? \\(\boldsymbol{\square}\\) cm what is the distance between the points a and a’? \\(\boldsymbol{\square}\\) cm

Explanation:

First Question: Distance between C and C'

Step1: Understand reflection property

In a vertical reflection over a horizontal line, the distance from a point to the line of reflection is equal to the distance from its image to the line. For point C, the distance to the line is 2 cm. So the distance from C to C' is twice that.

Step2: Calculate distance

Distance = 2 * 2 = 4 cm.

Step1: Find distance from B to bottom edge

The square has side length 3 cm, so the distance from B to the bottom edge (C's edge) is 3 cm.

Step2: Add distance from bottom edge to reflection line

The reflection line is 2 cm below the bottom edge, so total distance from B to reflection line is 3 + 2 = 5 cm.

Step1: Distance from A to reflection line

Distance from A to bottom edge is 3 cm (side length), plus 2 cm to reflection line: 3 + 2 = 5 cm.

Step2: Distance from A to A'

Since reflection, distance from A to A' is twice the distance from A to reflection line: 2 * 5 = 10 cm.

Answer:

4

Second Question: Perpendicular distance from B to reflection line