5.4 Solving Problems Involving Transformations

5.4 Solving Problems Involving Transformations

Example:

The diagram below shows the triangles ABC, SQT and PQR.

(a) Transformation T is a translation

(\begin{array}{l} 5 \\ - 2 \end{array})

Transformation P is a reflection in the straight line y = 7.

State the coordinates of the image of point A under each of the following transformations:

(i) Transformation T,

(ii) Combined transformation PT.

(b)

(i) PQR is the image of triangle ABC under the combined transformations MN. Describe in full, the transformation N and the transformation M.

(ii) Given that the area of the shaded region PSTR is 200 m², calculate the area of the triangle SQT.

Solution:
(a)

(i) A(3, 11) → T → A’(8, 9).

(ii) A(3, 11) → T → A’(8, 9) → P → A”(8, 5).

(b)(i)

N = Anticlockwise rotation of 90^o about the point B(5, 10).

(b)(ii)

M = Enlargement with centre (5, 12) and a scale factor of 3.

(c)

Area of image = (Scale factor)² x Area of object

Area of PQR = 3² x Area of SQT

Area of SQT + Area of PSTR = 9 x Area of SQT

Area of SQT + 200 = 9 x Area of SQT

200 = 9 x Area of SQT – Area of SQT

200 = 8 x Area of SQT

Area of S Q T = \frac{200}{8}

Area of SQT = 25 m²