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Question 10: Multiple Choice (Worth 2 points)

Triangle PQR has vertex coordinates at [tex]\( P(4, 0), Q(4, 3), \)[/tex] and [tex]\( R(5, 1) \)[/tex]. If the triangle is translated so that [tex]\( Q(0, 3) \)[/tex], determine the translation direction and number of units.

A. 4 units down
B. 4 units up
C. 4 units to the right
D. 4 units to the left



Answer :

GinnyAnswer
To determine the translation direction and number of units for the given triangle PQR:

1. Given Original Coordinates:
- Vertex P: (4, 0)
- Vertex Q: (4, 3)
- Vertex R: (5, 1)

2. Translated Coordinates:
- Translated Vertex Q: (0, 3)

3. Analyze the Change in Coordinates for Vertex Q:
- Original Q coordinate: (4, 3)
- Translated Q coordinate: (0, 3)

4. Calculate the Differences:
- Difference in the x-coordinate (Δx): [tex]\(0 - 4 = -4\)[/tex]
- Difference in the y-coordinate (Δy): [tex]\(3 - 3 = 0\)[/tex]

5. Interpret the Differences:
- The x-coordinate of Q changed by -4 units, which means Q moved 4 units to the left.
- The y-coordinate of Q remains the same (0 units of movement vertically).

Therefore, the translation for the triangle PQR to move vertex Q from (4, 3) to (0, 3) is 4 units to the left.

The correct answer is:
4 units to the left.