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Standard X

Mathematics

Reflection in the Origin

Using graph p...

Question

Using graph paper, plot the points $A (6, 4)$ and $B (0, 4)$ .
(i) Reflect $A$ and $B$ in the origin to get the images $A^{'}$ and $B^{'}$ .
(ii) Write the co-ordinates of $A^{'}$ and $B^{'}$ .
(iii) State the geometrical name for the figures $A B A^{'} B^{'}$ .
(iv) Find its perimeter.

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Solution

(i) Please See Graph.
(ii) Reflection of A' and B' in the origin $= A^{'} (- 6, - 4)$ and $B^{'} (0, - 4)$
(iii) The geometrical name for the figure ABA'B' is a parallelogram.
(iv) From the graph, AB $= 6$ cm, BB' $= 8$ cm.
In $Δ$ ABB'
$(A B^{'})^{2} = A B^{2} + (B B^{'})^{2}$
$= (6)^{2} + (8)^{2} = 36 + 64 = 100$
$A B^{'} = 10 = A^{'} B$ (ABA'B' is a parallelogram)
Perimeter of ABA'B'=A'B' $+$ AB' $+$ AB $+$ A'B
$= 6 + 10 + 6 + 10$
$= 32$ units.

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Using graph paper, plot the points A(6,4) and B(0,4).(i) Reflect A and B in the origin to get the images A′ and B′.(ii) Write the co-ordinates of A′ and B′.(iii) State the geometrical name for the figures ABA′B′.(iv) Find its perimeter.

Using graph paper, plot the points $A (6, 4)$ and $B (0, 4)$ .
(i) Reflect $A$ and $B$ in the origin to get the images $A^{'}$ and $B^{'}$ .
(ii) Write the co-ordinates of $A^{'}$ and $B^{'}$ .
(iii) State the geometrical name for the figures $A B A^{'} B^{'}$ .
(iv) Find its perimeter.