IB Mathematics Applications & Interpretation Question Type 1: Applying Transformations Given Descriptions Exercises

Point $C(-1,2)$ undergoes a horizontal stretch by factor 5, then a vertical stretch by factor 0.5, followed by a rotation of $180^{\circ }$ about the origin. Find the image of $C$.

Point $(3,5)$ undergoes a uniform enlargement of factor $k$, followed by a horizontal stretch of factor $k$, and then a vertical stretch of factor $m$, yielding $(27,25)$. Find $k$ and $m$.

A point $(5,2)$ is transformed by an enlargement of scale factor $k$, then a horizontal stretch by factor $k$, and then a vertical stretch by factor $m$, yielding the point $(45,30)$. Determine $k$ and $m$.

Point $D(3,-2)$ is first enlarged by factor $\frac{3}{2}$ about the origin, then stretched horizontally by factor 2, and finally rotated counterclockwise by $60^{\circ }$ about the origin. Find the final coordinates of $D$.

Point $B(1,-1)$ undergoes a horizontal stretch by factor 3, followed by a vertical stretch by factor 2, and then a counterclockwise rotation of $90^{\circ }$ about the origin. Determine the coordinates of the resulting point.

Point $A(2,3)$ is first stretched horizontally by factor 4, then enlarged uniformly by factor 2, and finally rotated counterclockwise by $120^{\circ }$ about the origin. Find the coordinates of the image of $A$.

A point $(2,3)$ is transformed by a uniform enlargement of scale factor $k$, followed by a horizontal stretch by factor $k$, and then a vertical stretch by factor $m$. The final image is $(8,12)$. Find the values of $k$ and $m$, given that $k$ and $m$ are positive constants.

Triangle $PQR$ has vertices $P(0,1)$, $Q(1,0)$ and $R(1,1)$. First apply an enlargement by factor 2 about the origin, then a horizontal stretch by factor $0.5$, and finally a counterclockwise rotation of $45^{\circ }$ about the origin. Find the coordinates of the transformed vertices $P^{\prime }$, $Q^{\prime }$ and $R^{\prime }$.

The point $(4,1)$ is subject to an enlargement with scale factor $k$ and centre $(0,0)$, followed by a stretch parallel to the $x$-axis with scale factor $k$, and then a stretch parallel to the $y$-axis with scale factor $m$. The resulting image is the point $(36,12)$.

Given that $k,m>0$, find the values of $k$ and $m$.

Point $(-2,4)$ undergoes a uniform enlargement of factor $k$, followed by a horizontal stretch of factor $k$, and then a vertical stretch of factor $m$. Its image is $(-18,24)$. Find $k$ and $m$.

The image of the point $(1,-4)$ after a uniform enlargement by factor $k$ (centered at the origin), followed by a horizontal stretch of factor $k$, and then a vertical stretch of factor $m$, is $(4,-28)$.

Find the value of $k$ and the value of $m$, given that $k>0$.

The line segment with endpoints $(2,0)$ and $(0,2)$ is transformed by a horizontal stretch by factor $2$, then by a uniform enlargement of scale factor $3$, and finally by a counterclockwise rotation of $270^{\circ }$ about the origin. Determine the coordinates of the transformed endpoints.