Coordinate Geometry

Answer the entire question on a graph paper.

Take a scale of $1 \; cm = 1 $ unit on both the axes.

  1. Plot point $A \left(6,6\right)$ and reflect it in the line $x = 0$ to obtain the point $A'$.

  2. Plot point $B \left(-3, 3\right)$ and reflect it in the $Y$ axis to obtain the point $B'$.

  3. Plot point $C \left(0,3\right)$ and reflect it in the line $y = -1$ to obtain the point $C'$.

  4. Join $A, \; C, \; A', \; B, \; C', \; B', \; A$ to form a geometric figure. Assign a name to the figure.

  5. Identify a point on the figure that is invariant on reflection in the line $x = 0$.


  1. Point $A \left(6, 6\right)$ reflected in the line $x = 0$ i.e. $Y$ axis gives the point $A' \left(-6,6\right)$.

  2. Point $B \left(-3, 3\right)$ reflected in the $Y$ axis gives the point $B' \left(3,3\right)$.

  3. Point $C \left(0, 3\right)$ reflected in the line $y = -1$ gives the point $C' \left(0, 5\right)$.

  4. The geometric figure $ACA'BC'B'A$ is an arrow.

  5. The points $C \left(0, 3\right)$ and $C' \left(0, -5\right)$ on the figure are invariant on reflection in the line $x = 0$.