8. Plot P(0, 2) and Q(3, 2). Reflect P in the x-axis
to get P' and reflect Q in the origin to get Q.
(1) Write the co-ordinates of P' and Q'.
(ii) What is the geometrical figure formed
by joining PQP'Q?
(iii) Find its perimeter and area.
(iv) Name two points from the figure which
are invariant on reflection in y-axis.
Answers
Step-by-step explanation:
A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.
Solution 2
Since, the point P is its own image under the reflection in the line l. So, point P is an invariant point.
Hence, the position of point P remains unaltered.
Question 3
State the co-ordinates of the following points under reflection in x-axis:
(i) (3, 2)
(ii) (-5, 4)
(iii) (0, 0)
Solution 3
(i) (3, 2)
The co-ordinate of the given point under reflection in the x-axis is (3, -2).
(ii) (-5, 4)
The co-ordinate of the given point under reflection in the x-axis is (-5, -4).
(iii) (0, 0)
The co-ordinate of the given point under reflection in the x-axis is (0, 0).
Answer:
To find the co-ordinates in the adjoining figure, x-axis represents the plain mirror. M is the point in the rectangular axes in the first quadrant whose co-ordinates are (h, k).
Reflection in x-axis
1Save
When point M is reflected in x-axis, the image M’ is formed in the fourth quadrant whose co-ordinates are (h, -k). Thus we conclude that when a point is reflected in x-axis, then the x-co-ordinate remains same, but the y-co-ordinate becomes negative.
Thus, the image of point M (h, k) is M' (h, -k).
Rules to find the reflection of a point in the x-axis:
(i) Retain the abscissa i.e., x-coordinate.
(ii) Change the sign of ordinate i.e., y-coordinate.
Examples to find the co-ordinates of the reflection of a point in x-axis:
1. Write the co-ordinates of the image of the following points when reflected in x-axis.
(i) (-5 , 2)
(ii) (3, -7)
(iii) (2, 3)
(iv) (-5, -4)
Solution:
(i)The image of (-5 , 2) is (-5 , -2).
(ii) The image of (3, -7) is (3, 7).
(iii) The image of (2, 3) is (2, -3).
(iv) The image of (-5, -4) is (-5, 4).
2. Find the reflection of the following in x-axis:
(i) P (-6, -9)
(ii) Q (5, 7)
(iii) R (-2, 4)
(iv) S (3, -3)
Solution:
The image of P (-6, -9) is P' (-6, 9).
The image of Q (5, 7) is Q' (5, -7) .
The image of R (-2, 4) is R' (-2, -4) .
The image of S (3, -3) is S' (3, 3) .
Solved example to find the reflection of a triangle in x-axis:
3. Draw the image of the triangle PQR in x-axis. The co-ordinate of P, Q and R being P (2, -5); Q (6, -1); R (-4, -3)
Solution:
Reflection of a Point in x-axis
1Save
Plot the points P (2, -5); Q (6, -1); R (-4, -3) on the graph paper. Now join PQ, QR and RP; to get a triangle PQR.
When reflected in x-axis, we get P' (2, 5); Q' (6, 1); R' (-4, 3). Now join P'Q', Q'R' and R'P'.
Thus, we get a triangle P'Q'R' as the image of the triangle PQR in x-axis.
Solved example to find the reflection of a line-segment in x-axis:
4. Draw the image of the line segment PQ having its vertices P (-3, 2), Q (2, 7) in x-axis.
Solution:
Reflection of a Line-segment in x-axis
1Save
Plot the point at P (-3, 2) and at Q (2, 7) on the graph paper. Now join P and Q to get the line segment PQ.
When reflected in x-axis P (-3, 2) become P' (-3, -2) and Q (2, 7) become Q' (2, -7) on the same graph. Now join P'Q'.
Therefore, P'Q' is the image of PQ when reflected in x-axis.
Note: Point M (h, k) has image M' (h, -k) when reflected in x-axis.
Thus, we conclude that when the reflection of a point in x-axis:
x-axis acts as a plane mirror.
M is the point whose co-ordinates are (h, k).
The image of M i.e. M' lies in fourth quadrant.
The co-ordinates of M' are (h, -k
Step-by-step explanation:
please mark as brain list