Shape and Space 5
4 marks · HardA triangle has vertices at (1, 1), (3, 1), and (1, 4). The triangle is first reflected in the line y = x, and then the image is translated by the vector .
Write down the coordinates of the triangle after the reflection.
Write down the coordinates of the triangle after the translation.
Write down the coordinates of the triangle after the translation.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Coordinates of reflected triangle: (1,1), (1,3), (4,1) · must show (1,1), (1,3), (4,1)
(b) Coordinates after translation: (-1,2), (-1,4), (2,2) · must show (-1,2), (-1,4), (2,2)
Common mistakes: Incorrect reflection over y = x (swap not invert coordinates); Translation in wrong direction
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly reflects at least one vertex in y = x
A1 (a) · 1 mark · All three vertices of the triangle reflected correctly
M2 (b) · 1 mark · Uses the translation vector correctly on at least one point
A2 (b) · 1 mark · All three vertices of the triangle translated correctly
Worked solution
First, reflect each vertex in the line y = x by swapping the x- and y-coordinates:
| Original | Reflected |
|---|---|
| (1, 1) | (1, 1) |
| (3, 1) | (1, 3) |
| (1, 4) | (4, 1) |
Then translate each point by . This means subtract 2 from x and add 1 to y:
| Reflected | Translated |
|---|---|
| (1, 1) | (-1, 2) |
| (1, 3) | (-1, 4) |
| (4, 1) | (2, 2) |