Transformations — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Reflecting in the x-axis keeps the x-coordinate and negates the y-coordinate.

(3, −5)

Question 2

(a)Add the vector's components to the point's coordinates.

(2+3, 4−1) = (5, 3)

Question 3

(a)Multiply both coordinates by the scale factor.

(1×3, 2×3) = (3, 6)

Question 4

(a)Reflecting in the y-axis negates the x-coordinate, keeps y the same.

(−4, −2)

Question 5

(a)A 180° rotation about the origin negates both coordinates.

(−3, 5)

Question 6

(a)Add the vector's components to the point.

(−1+4, 3+2) = (3, 5)

Question 7

(a)New point = centre + scale factor × (point − centre).

(1+2(2−1), 1+2(−1−1)) = (3, −3)

Question 8

(a)Reflecting in the x-axis negates the y-coordinate.

(0, −5)

Question 9

(a)Apply the rule (x,y)→(−y,x).

(−2, 3)

Question 10

(a)The x-coordinate is unchanged and the y-coordinate is negated — this is a reflection in the x-axis.

Reflection in the x-axis

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