M L Aggarwal Solutions for Exercise 3: Chapter Test

The point $P\left(4, -7\right)$ on reflection in $x$-axis is mapped onto $P\text{'}$. Then $P\text{'}$ on reflection in the $y$-axis is mapped onto $P\text{'}\text{'}$. Find the coordinates of $P\text{'}$ and $P\text{'}\text{'}$. Write down a single transformation that maps $P$ onto $P\text{'}\text{'}$.

The point $P\left(a, b\right)$ is first reflected in the origin and then reflected in the $y$ axis to $P\text{'}$. If $P\text{'}$ has coordinates $\left(3, -4\right)$, evaluate $a, b$.

A point $P\left(a, b\right)$ becomes $\left(-2, c\right)$ after reflection in the $x$-axis, and $P$ becomes $\left(d, 5\right)$ after reflection in the origin. Find the values of $a, b, c$ and $d$.

$A\left(4, -1\right), B\left(0, 7\right)$ and $C\left(-2, 5\right)$ are the vertices of a triangle. $△ABC$ is reflected in the $y$-axis and then reflected in the origin. Find the coordinates of the final images of the vertices.

The points $A\left(4, -11\right), B\left(5, 3\right), C\left(-2, 5\right)$ and $D\left(1, 1\right)$ are the vertices of a parallelogram. If the parallelogram is reflected in the $y$-axis and then in the origin, find the coordinates of the final images. Check whether it remains a parallelogram. Write down a single transformation that brings the above change.

Use a graph paper for this question (take $2 \mathrm{cm}=1$ unit on both $x$ and $y$ axes).

$\left(i\right)$ Plot the following points: $A\left(0, 4\right), B\left(2, 3\right), C\left(1, 1\right)$ and $D\left(2, 0\right)$.

$\left(ii\right)$ Reflect points $B, C, D$ on $y$-axis and write down their coordinates. Name the images as $B\text{'}, C\text{'}, D\text{'}$ respectively.

$\left(iii\right)$ Join points $A, B, C, D, D\text{'}, C\text{'}, B\text{'}$ and $A$ in order, so as to form a closed figure. Write down the equation of line of symmetry of the figure formed.

The triangle $OAB$ is reflected in the origin $O$ to triangle $OA\text{'}B\text{'}$. $A\text{'}$ and $B\text{'}$ have coordinates $\left(-3, -4\right)$ and $\left(0, -5\right)$ respectively. 

(i) Find the co-ordinates of $A$and $B.$

(ii) Draw a diagram to represent the given information. 

(iii) What kind of figure is the quadrilateral $ABA\text{'}B\text{'}?$

(iv) Find the coordinates of $A",$the reflection of A in the origin followed by reflection in the y-axis.

(v) Find the co-ordinates of $B\text{'},$ the reflection of $B$ in the $x-$axis followed by reflection in the origin.