Question

Hola Brainlians!!

A simple question for you all.

Using a graph paper, plot the points A(6,4)
and B(0,4).
(a) Reflect A and B in the origin to get the images A' and B'.

(b) Write the co-ordinates of A' and B'.

(C) State the geometrical name for the figure ABA'B'.

(d) Find its perimeter.

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Answer 1

Question :-

Using a graph paper, plot the points A(6,4)

and B(0,4).

(a) Reflect A and B in the origin to get the images A' and B'.

(b) Write the co-ordinates of A' and B'.

(c) State the geometrical name for the figure ABA'B'.

(d) Find its perimeter.

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Solution :-

➲ Given Information :-

• Co-ordinates of point A ➢ A(6 , 4)
• Co-ordinates of point B ➢ B(0 , 4)

➲ To Find :-

• (a) Reflect A and B in the origin to get the images A' and B'.

• (b) Write the co-ordinates of A' and B'.

• (c) State the geometrical name for the figure ABA'B'.

• (d) Find its perimeter.

➲ Concept :-

• Co-ordinate Geometry - Reflection

➲ Explanation :-

• The reflection of points A and B will lie on the Third Quadrant. The reflection of point A will be in Third quadrant and reflection of point B will be on the Y-axis. We'll count the number of Units between Point A and B and Origin, We will be able to determine that where, our reflection will lie. Now let's proceed towards our answers.

➲ Answers & Calculation :-

• Answer (a) - In order to get the the image of points A and B, Kindly refer to the image attached above.

• Answer (b) -

1. Co-ordinates of A' = (-6 , -4)
2. Co-ordinates of B' = (0 , -4)

• Answer (c) - The geometrical name for the figure ABA'B' is Parallelogram. As, if a line is drawn from A to B to A' and B', line segment AB will be parallel to line segment A'B'. And line segment A'B will be parallel to line segment AB'.

• Answer (d) - The perimeter of the figure ( Parallelogram ) is 32 units.

➲ Diagram :-

• The diagram is provided in the image attached above. Make sure to check it for answer (a).

Calculation :-

In Parallelogram ABA'B',

○ Measure of BB' = 8 units

○ Measure of A'B' = 6 units

∴ BA' = $\sf \sqrt{ {6}^{2} + {8}^{2} }$

:⇒ BA' = $\sf \sqrt{ 36 + 64 }$

:⇒ BA' = $\sf \sqrt{ 100 }$

:⇒ BA' = $\sf {\red{10\: units}}$

And since BA' is parallel to AB', therefore,

AB' = $\sf {\red{10 \: units}}$

We know,

AB = A'B' = $\sf {\red{6 \: units}}$

∴ The Perimeter of Parallelogram ABA'B' = AB + BA' + A'B' + AB'

:⇒ The Perimeter of Parallelogram ABA'B' = ( 6 + 10 + 6 + 10 ) units

:⇒ The Perimeter of Parallelogram ABA'B' = 32 units

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Final Answers :-

• (a) Reflect A and B in the origin to get the images A' and B'. -

Refer diagram

• (b) Write the co-ordinates of A' and B'. -

Co-ordinates of A' = (-6 , -4)

Co-ordinates of B' = (0 , -4)

• (c) State the geometrical name for the figure ABA'B'. -

Parallelogram

• (d) Find its perimeter.

The Perimeter of Parallelogram ABA'B = 32 units

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Answer 2

➲Question:-

Using a graph paper, plot the points A(6,4) and B(0,4).

‎

(a) Reflect A and B in the origin to get the

images A' and B'.

(b) Write the co-ordinates of A' and B

(C) State the geometrical name for the figure ABA'B'.

(d) Find its perimeter.

‎

➲Answer:-

• ➲*(A) Answer is in attachment

(B) Co - oridinates Of À = ( -6,-4) Co- oridinates Of B' = (0,-4)

‎

(C) ABA'B' is parallelogram.

‎

(D) In ABA'B ,BB' = 8 units, A'B' = 6 units

‎

$∴BA! = \sqrt{6 {}^{2} + 8 {}^{2} } = \sqrt{36 + 64} = \sqrt{100} = 10 \: units$

$➲∴BA! = 10 \: units$

‎

AB = A'B = 6 units

• ∴ the perimeter of ABA'B' = AB + BA' +A'B + B'A

= 6 + 10 + 6+ 10

= 32 units

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‎#Be Brainly ༄