Question

[Maths]
Question in Attachment.

Topic: Reflection (Coordinate Geometry)

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Answer 1

Topic :-

Coordinate Geometry

Question :-

P and Q have coordinates (0, 5) and (-2, 4).

(a) P is invariant when reflected in an axis. Name the axis.

(b) Find the image of Q on reflection in the axis found in (a).

(c) (0, k) on reflection in the origin is invariant. Write the value of k.

(d) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin follówed by reflection in X-axis.

Solution :-

(a) Point P (0, 5) lies on Y-axis. Hence, when point P will be reflected in Y-axis then point P will be invariant.

(b) When any point (a, b) is reflected in Y-axis then coordinates of its image formed is (-a, b).

Thus, coordinates of image of point Q (-2, 4) after reflection in Y-axis will be (2, 4).

(c) When any point (a, b) is reflected in origin then coordinates of its image formed is (-a, -b).

Reflection of (0, k) in origin will be (0, -k).

It is given that, reflection of point (0, k) in origin is invariant which means x coordinate and y coordinate remains same after reflection.

Thus,

k = -k

k + k = 0

2k = 0

k = 0

So, the value of k is 0.

(d) It is given that point Q (-2, 4) is reflected in origin first, which means coordinates of its image formed will be (2, -4) as when any point (a, b) is reflected in origin then coordinates of its image formed is (-a, -b).

Finally, image (2, -4) is reflected in X-axis. When any point (a, b) is reflected in X-axis then coordinates of its image formed is (a, -b).

Thus, coordinates of image of point (2, -4) when reflected in X-axis will be (2, 4).

Answer :-

(a) Y-axis

(b) (2, 4)

(c) 0

(d) (2, 4)

Answer 2

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1. y axis
2. (2,4)
3. k=0
4. (2,4)