Question Type 1: Applying transformations given descriptions Exercises

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 $(4,1)$ is subject to an enlargement of factor $k$, then a horizontal stretch by factor $k$, and then a vertical stretch by factor $m$, resulting in the point $(36,12)$. Determine $k$ and $m$.

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 $m$.

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

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 $m$.

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 $(-2,4)$ 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 $m$.

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 $A$.

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.

Point $D(3,-2)$ is first enlarged by factor $\tfrac32$ about the origin, then stretched horizontally by factor 2, and finally rotated counterclockwise by $60^\circ$ about the origin. Find the final coordinates of $D$.

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 $P'$, $Q'$ and $R'$.