A point $P (- 8, 1)$ is reflected in the $x$ -axis to the point $P^{'}$ . The point $P^{'}$ is then reflected in the origin to point $P^{''}$ . Write down the co-ordinates of $P^{''}$ . State the single transformation that maps $P$ into $P^{''}$ .

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Solution

Step $1$ : Find the co-ordinates of $P^{'}$

Given: Co-ordinates of $P = (- 8, 1)$

$P$ is reflected in the $x$ -axis to the point $P^{'}$ .

Reflection in the $x$ -axis, $M_{x} (x, y) = (x, - y)$

$\Rightarrow M_{x} (- 8, 1) = (- 8, - 1)$

So, the co-ordinates of $P^{'}$ are $(- 8, - 1)$ .

Step $2$ : Find the co-ordinates of $P^{''}$

$P^{'}$ is reflected in the origin to point $P^{''}$ .

Reflection in the origin, $M_{o} (x, y) = (- x, - y)$

$\Rightarrow M_{o} (- 8, - 1) = (8, 1)$

So, the co-ordinates of $P^{''}$ are $(8, 1)$ .

Step $3$ : State the single transformation that maps $P$ into $P^{''}$

Co-ordinates of $P = (- 8, 1)$

Co-ordinates of $P^{''} = (8, 1)$

On reflection, only the sign of the abscissa
( $x$ -coordinate) has changed.

Reflection in the $y$ -axis, $M_{y} (x, y) = (- x, y)$

Hence, the single transformation that maps $P$ onto $P^{''}$ is reflection in the $y$ -axis.

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Reflection

Standard VI Mathematics

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A point P(−8,1) is reflected in the x-axis to the point P′. The point P′ is then reflected in the origin to point P′′. Write down the co-ordinates of P′′. State the single transformation that maps P into P′′.

A point $P (- 8, 1)$ is reflected in the $x$ -axis to the point $P^{'}$ . The point $P^{'}$ is then reflected in the origin to point $P^{''}$ . Write down the co-ordinates of $P^{''}$ . State the single transformation that maps $P$ into $P^{''}$ .