Question

Use graph paper to answer this question. $A (4, 6)$ and $B (1, 2)$ are two points. $A'$ is the image of $A$ when reflected in the $x$ -axis. $B'$ is the image of $B$ when reflected in the line $A A'$ . Draw $A B A' B'$ Give the geometrical name for the figure $A B A' B'$ .

Accepted Answer

First we shall obtain the reflection of the point $A (4, 6)$ in the $B (1, 2)$ -axis.

We know that when a point is reflected in the $x$ -axis,

(i) both the magnitude and the sign of the $A'$ -coordinate remains the same.

(ii) the magnitude of the $y$ -coordinate remains the same but, its sign changes.

Thus, if the coordinate of a point is $B'$ , then the coordinate of its image under reflection in the $A A'$ -axis is $(x, - y)$ .

Therefore, the coordinate of the image of the point $A (4, 6)$ under reflection in the $x$ -axis is $A' (4, - 6)$ .

Now, join $A A'$ .

The line $A A'$ is parallel to $y$ -axis at a distance of $4$ units towards its right. So, the equation of the line $A A'$ will be $x = 4$ .

Now, we shall obtain the image of the point $B (1, 2)$ in this line $x = 4$ .

The coordinates of the image of $B$ is $(- x + 2 a, y)$ .

Here, the values of $x = 1, y = 2$ and $a = 4$ .

So, the coordinate of the image of $B$ is $(- x + 2 a, y) = (- 1 + 2 \times 4, 2) = (7, 2)$ .

Therefore, the coordinate of the image is $B' (7, 2)$ .

Now, we join $A B, B A', A' B'$ and $B' A$ . The resulting figure $A B A' B'$ is a kite.

M L Aggarwal Solutions for Exercise 1: Exercise 10

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 1: Exercise 10

Questions from M L Aggarwal Solutions for Exercise 1: Exercise 10 with Hints & Solutions

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