Name: Problem Based on Reflection of Point
Uploaded: 2019-07-19
Duration: 8 min 33 s
Description: In this video, we will learn to solve a problem based on the reflection of a point. Watch this video, grab a pen and paper, and start solving the problem.

Question

Points $A$ and $B$ have coordinates $(2, 5)$ and $(0, 3)$ . $A'$ is the image of $A$ under reflection in the $x$ -axis. Find the image $B'$ of $B$ under reflection in the line $A A'$ .

Accepted Answer

We are given to find the coordinates of the image of $A (2, 5)$ under reflection in $x$ -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 $A (2, 5)$ under reflection in the $x$ -axis is $A' (2, - 5)$ .

Now, we shall find the image $B'$ of $B (0, 3)$ under reflection in the line $A A'$ .

We join the points $A$ and $A'$ .

We observe that the line $A A'$ is parallel to $y$ -axis at a distance of $2$ units towards the right of the origin (The equation of the line is $x = 2$ ).

We know that the reflection of the point $P (x, y)$ in the line $x = a$ is the point $P' (- x + 2 a, y)$ .

So, here, $x = 0, y = 3$ and $a = 2$ .

So, the coordinate of the image of $A'$ is $(- x + 2 a, y) = (- 0 + 2 \times 2, 3) = (4, 3)$ .

Therefore, the coordinate of $B'$ is $(4, 3)$ .

Points $A$ and $B$ have coordinates $(2, 5)$ and $(0, 3)$ . $A'$ is the image of $A$ under reflection in the $x$ -axis. Find the image $B'$ of $B$ under reflection in the line $A A'$ .

Important Questions on Reflection

Learn and Prepare for any exam you want !

Points A and B have coordinates 2,5 and 0,3. A' is the image of A under reflection in the x-axis. Find the image B' of B under reflection in the line AA'.

Important Questions on Reflection

Learn and Prepare for any exam you want !

Points $A$ and $B$ have coordinates $(2, 5)$ and $(0, 3)$ . $A'$ is the image of $A$ under reflection in the $x$ -axis. Find the image $B'$ of $B$ under reflection in the line $A A'$ .