[3 marks sum]

Question 13 Marks

Point $A ( 4,-1)$ is reflected as A' in the line $x= 1.$ Point B on reflection in the line $y=3$ is mapped as $B' (6,-1).$ Write the co-ordinates of A' and B. Write the co-ordinates of mid.-ooint of the line sgment A' B'.

Answer

$A(4,-1)$, the co-ordinates of $A^{\prime}=(2 \times 1-4,-1)=(-2,-1)$
$A^{\prime}(6,-1)$, the co-ordinatesof $B=(6,2 \times 3-(-1))=(6,7)$
The distance between $A ^{\prime} B ^{\prime}$
$=\sqrt{(6-(-2))^2+(-1-(-1))^2} $
$=\sqrt{8^2+0} $
$=8 \text { units }$
Distance till midpoin $t =4$ units
Co-ordinates of mid-point $=(-2+4,-1+4)=(2,3)$

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Question 23 Marks

Point $A (1 , -5)$ is mapped as A' on rflection in the line $y = 1.$ The point $B (-5 , 1)$ is mapped as B' on reflection in the line $y = 4.$ Write the co-ordinaes of A' and B' . Calculate AB'.

Answer

$A(1,-5)$, he co-ordinate of $A^{\prime}=(1,2 \times 1-(-5))=(1,7)$
$B(-5,1)$, the co-ordinate of $B^{\prime}=(-5,2 \times 4-(1))=(-5,7)$
The distance $A B^{\prime}=\sqrt{(-5-1)^2+(7-(-5))^2}$
$=\sqrt{(-6)^2+12^2}$
$=\sqrt{36+144} $
$=\sqrt{180} $
$=13.41 \text { units }$

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Question 33 Marks

A triangle ABC lies in the co-ordinate plane. The co-ordinates of its vertices are A (2, 3), B ( 4,-4) and C (6 ,-7). This triangle is reflected in the line y=O onto LA'B'C'. LA'B'C' is then reflected in the origin ontolA"B"C". Write down the co-ordinates of LA'B'C' and LA "B" C".

Answer

A = (2, 3); B = (4,-4); C = (6,-7)
Co-ordinates of LA'B'C' under reflection in the line y=O:
A'= (2,-3); B' = (4, 4); C' = (6, 7)
Co-ordinates of LA "B" C" under reflection in the origin :
A"= (-2, 3);B" = (-4,-4); C" = (-6,-7)

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Mathematics [3 marks sum]

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