Similar Figures Practice

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An illustration shows four right-angled triangles labeled Figure 1 through Figure 4 placed in various positions on a 12 column by 10 row grid. Figures 1, 2, and 4 are the same size while Figure 3 is slightly larger. Figure 1 is a right-angled triangle with the base left vertex on the bottom of the 4th row and the start of the 4th column. The base right vertex is on the bottom of the 4th row and the end of the 5th column. The base constitutes 2 units on the grid. The top vertex is on top of the 2nd row and the start of 4th column. The perpendicular height constitutes 3 units on the grid. Figure 2 is a right-angled triangle with the base left vertex on the bottom of the 4th row and the start of the 9th column. The base right vertex is on the bottom of the 4th row and the end of the 10th column. The top vertex is on the top of the 2nd row and end of 10th column. The hypotenuse is between top vertex and bottom left. Figure 3 is a right-angled triangle with the base left vertex on the bottom of the 7th row and the start of 7th column. The base right vertex is on the bottom of the 7th row and the end of the 9th column. The base constitutes 3 units on the grid. The top vertex is on the top of the 4th row and start of 7th column. The hypotenuse is between top vertex and bottom left. The perpendicular height constitutes 4 units on the grid. Figure 4 is a right-angled triangle with the top left vertex on the top of the 7th row and start of the 4th column. The top right vertex in on the top of the 7th row and the end of the 5th column. The bottom vertex is on the bottom of the 9th row and start of 4th column. The hypotenuse is between top right vertex and bottom vertex.

Which figure would result from reflecting Figure 1 over a vertical line?

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Figure
Remaining Attempts : 3

Answer 1

To determine which figure would result from reflecting Figure 1 over a vertical line, we need to analyze the position and shape of Figure 1.

Figure 1 is a right-angled triangle with:

• Base left vertex: (4, 4)
• Base right vertex: (5, 4)
• Top vertex: (4, 2)

When we reflect this triangle over a vertical line, the x-coordinates of the vertices will change while the y-coordinates will remain the same. Specifically, if we reflect it across a vertical line that is centered between the base vertices at the x-coordinate of \(4.5\), we will calculate the new positions of the vertices:

1. Base left vertex (4, 4) reflected would become (5, 4).
2. Base right vertex (5, 4) reflected would become (4, 4).
3. The top vertex (4, 2) reflected would become (5, 2).

Reflecting across the vertical line effectively switches the base left and right vertices, while the top vertex's x-coordinate also changes accordingly.

Now, based on the information provided about the position of the other figures, we can conclude that the new set of vertices (5, 4), (4, 4), and (5, 2) does correspond to one of the other figures, likely to Figure 2 or Figure 4 since they share similar configurations described in the question.

To confirm which one corresponds directly, we compare their coordinates after reflection: If we consider Figure 2:

• Base left vertex: (9, 4)
• Base right vertex: (10, 4)
• Top vertex: (10, 2)

And for Figure 4, the relevant vertices would need to align with the reflected vertices—which gives a better match.

Therefore, based on this analysis, the answer is:

Figure 2 would result from reflecting Figure 1 over a vertical line.