Question

two shapes are represented on a coordinate grid.
which sentence about the two shapes must be true?
the two shapes are congruent because shape 1 can be translated down 3 units and to the right 1 unit to make shape 2.
the two shapes are congruent because shape 1 can be translated down 3 units and to the right 4 units to make shape 2.
the two shapes are similar but not congruent because shape 1 can be translated down 3 units and to the right 1 unit to make shape 2.
the two shapes are similar but not congruent because shape 1 can be translated down 3 units and to the right 4 units to make shape 2.

Explanation:

Step1: Understand Congruence and Translation

Congruent shapes have the same size and shape. Translation is moving a shape without resizing or rotating.

Step2: Check the Horizontal Translation

Count the units moved right. Shape 1 moves from \(x = 1\) (approximate left - most point) to \(x = 5\) (approximate left - most point of shape 2). The horizontal translation is \(5 - 1=4\) units to the right.

Step3: Check the Vertical Translation

Count the units moved down. Shape 1 has a point at \(y = 6\) (approximate lower - most point) and shape 2 has a point at \(y = 3\) (approximate lower - most point). The vertical translation is \(6 - 3 = 3\) units down.

Step4: Check Congruence

Since translation (a rigid transformation) is used and no resizing occurs, the shapes are congruent.

Answer:

B. The two shapes are congruent because shape 1 can be translated down 3 units and to the right 4 units to make shape 2.