Question

Use the image to answer the question.

A coordinate plane with 4 quadrants shows x and y axes ranging from negative 5 to 5 in increments of 1. Three triangles are formed by joining three plotted points each. Two of the triangles are joined by connecting their vertices with rays. The coordinates of the plotted points for the triangle in quadrant 4 are left parenthesis 1 comma negative 1 right parenthesis, left parenthesis 1 comma negative 3 right parenthesis, and left parenthesis 3 comma negative 2 right parenthesis. The coordinates for the triangle in quadrant 2 are left parenthesis negative 4 comma 2 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, and left parenthesis negative 3 comma 4 right parenthesis. The side joining point left parenthesis negative 4 comma 2 right parenthesis and point left parenthesis negative 2 comma 2 right parenthesis is labeled e. The side joining point left parenthesis negative 4 comma 2 right parenthesis and point left parenthesis negative 3 comma 4 right parenthesis is labeled g. The side joining point left parenthesis negative 3 comma 4 right parenthesis and point left parenthesis negative 2 comma 2 right parenthesis is labeled h. The coordinates of the plotted points for the triangle in quadrant 1 are left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 1 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. Three rays join each vertex of the triangle in quadrant 1 to the complementary vertices of the triangle in quadrant 2. A ray connects point left parenthesis 1 comma 1 right parenthesis to point left parenthesis negative 4 comma 2 right parenthesis. A ray connects point left parenthesis 3 comma 1 right parenthesis to point left parenthesis negative 2 comma 2 right parenthesis. A ray connects point left parenthesis 2 comma 3 right parenthesis to point left parenthesis negative 3 comma 4 right parenthesis. The arrow heads are on the vertices of the triangle in quadrant 2.

What two transformations are shown to demonstrate that the triangles are congruent?

(2 points)
degrees counterclockwise and (
,
)​​​​​​​
Sorry, that’s only partially correct

Look at how far the shape in Quadrant II moves left or right to match the shape in Quadrant I. Record the x-value.
Remaining Attempts : 2
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Answer 1

To determine the transformations that show the congruence of the triangles in Quadrant I and Quadrant II, we can analyze the positions of the triangles:

1. **Translation**: To move the triangle from Quadrant II to Quadrant I, the x-coordinates of the points in Quadrant II need to be adjusted. The triangle in Quadrant II has points with x-coordinates of -4, -2, and -3. To find out how far we need to translate them to match the x-coordinates of the triangle in Quadrant I, we observe that:
- The point in Quadrant I with the corresponding x-coordinate of 1 (which is the same y-coordinate as the point in Quadrant II with x-coordinate -4) indicates a horizontal movement of 5 units to the right.

Thus, the x-value for the translation is +5.

2. **Rotation**: The triangles must also be rotated. Observing their orientations, if one triangle is rotated around the origin, it can align with the other. The exact degree of rotation would depend on the specific angles of the triangles—a common conjecture in such transformations is 90 degrees counterclockwise.

In summary, the two transformations are:
- **Translation**: 5 units to the right (or +5 in x-direction).
- **Rotation**: 90 degrees counterclockwise.

So, the answer will be:
- Degrees counterclockwise: 90 degrees
- X-value for translation: +5