Question

Hola Brainlians!!

A simple question for you all.
Use graph paper for this question.

(Take 2 cm=1 unit along both X-axis and
y-axis.)

Plot the points O(0, 0), A(-4,4), B(-3, 0) and
C(0, -3)

(i) Reflect points A and B· on the y-axis and
name them A' and B' respectively. Write
down their co-ordinates.

(ii) Name the Figure OABCB'A'

(iii) State the line of symmetry of this figure.
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Answer 1

Question :-

(Take 2 cm=1 unit along both X-axis and

y-axis.)

Plot the points O(0, 0), A(-4,4), B(-3, 0) and

C(0, -3)

(i) Reflect points A and B· on the y-axis and name them A' and B' respectively. Write down their co-ordinates.

(ii) Name the Figure OABCB'A'

(iii) State the line of symmetry of this figure.

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

Solution :-

➲ Given Information :-

• Scale ➢ 2 cm = 1 unit in both X-axis and Y-axis
• Point O ➢ O(0 , 0)
• Point A ➢ A(-4 , 4)
• Point B ➢ B(-3 , 0)
• Point C ➢ C(0 , -3)

➲ To Find :-

• (i) Reflect points A and B· on the y-axis and name them A' and B' respectively. Write down their co-ordinates.

• (ii) Name the Figure OABCB'A'

• (iii) State the line of symmetry of this figure.

➲ Concept :-

• Co-ordinate Geometry - Reflection

➲ Diagram :-

• The diagram is provided in the image attached above. Make sure to check it for better understanding.

➲ Explanation :-

• Reflection of points A and B which originally lie in second quadrant and X-axis respectively will lie in first quadrant and X-axis respectively. Point C will remain on the Y-axis. We will be connecting all the points beginning from point A to point B to point C to point B' to point A' to point O and from point O to point A back again. Just for reference we will be drawing Vertical lines from point A and A' to X-axis and Horizontal lines from point A to A'. Now let's proceed towards our Answers.

➲ Answers :-

• Answer (i) -

➽ Reflection of point A i.e., A' = A'(4 , 4)

➽ Reflection of point B i.e., B' = B'(3 , 0)

• Answer (ii) -

➽ The name of the figure OABCB'A' is Arrow Head.

• Answer (iii) -

➽ The line of symmetry for the figure OABCB'A' is the Y-axis as it completely divides the figure into two equal, congruent halves.

➽ An image of half divided Arrow Head is given above. Do refer it if you are interested to see it.

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

Final Answers :-

• (i) Reflect points A and B· on the y-axis and name them A' and B' respectively. Write down their co-ordinates.

Answer )- Reflection of point A i.e., A' = A'(4 , 4)

Reflection of point B i.e., B' = B'(3 , 0)

• (ii) Name the Figure OABCB'A'

Answer )- The name of the figure OABCB'A' is Arrow Head.

• (iii) State the line of symmetry of this figure.

Answer )- The line of symmetry for the figure OABCB'A' is the Y-axis.

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

Answer 2

Answer:

• Below

Step-by-step explanation:

(i) The points A (3, 5) and B (-2, -4) can be plotted on a graph as shown.

(ii) A’ = Image of A when reflected in the x-axis = (3, -5)

(iii) C = Image of B when reflected in the y-axis

= (2, -4)

B’ = Image when C is reflected in the origin

= (-2, 4)

(iv) Isosceles trapezium

(v) Any point that remains unaltered under a given transformation is called an invariant.

Thus, the required two points are (3, 0) and (-2, 0).