Question

Triangle LMN is located at L (2, 3), M (1, 2), and N (4, 4). The triangle is then transformed using the rule (x+5, y+2) to form the image L'M'N'. What are the new coordinates of L', M', and N'?

Answer 1

Given :- Triangle LMN is located at L (2, 3), M (1, 2), and N (4, 4). The triangle is then transformed using the rule (x+5, y+2) to form the image L'M'N'.

To Find :-

• What are the new coordinates of L', M', and N' ?

Solution :-

Rule for x - axis Points = (x + 2) .

Therefore, New x - axis points of new ∆ are :-

• L' = 2 + 5 = 7
• M' = 1 + 5 = 6
• N' = 4 + 5 = 9 .

and, Rule for y - axis Points = (y + 2) .

Therefore, New y - axis points of new ∆ are :-

• L' = 3 + 2 = 5
• M' = 2 + 2 = 4
• N' = 4 + 2 = 6 .

Hence, New coordinates of L', M', and N' :-

• L' = (7 , 5)
• M' = (6, 4)
• N' = (9, 6)

[ Refer To image also. ]

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Answer 2

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GIVEN

1. Triangle LMN is located at

L (2, 3), M (1, 2), and N (4, 4).

2. The triangle is then transformed using

the rule (x+5, y+2) to form the image L'M'N'

TO DETERMINE

The new coordinates of L', M', and N'

CONCEPT TO BE IMPLEMENTED

CHANGE OF ORIGIN WITHOUT CHANGE OF DIRECTION OF AXES

Let ( x , y ) be the coordinates of a point P

with respect to the rectangular axes

OX and OY

Let ( h , k ) be the coordinates of the new

origin O' with respect to the rectangular

axes OX and OY

Let ( x' , y' ) be the coordinates of the same

point P with respect to the new rectangular

axes OX' and OY'

Then x = x' + h and y = y' + k

In other words by transformation ( x, y )

transformed into ( x - h, y - k )

CALCULATION

It is given that Triangle LMN is located at

L (2, 3), M (1, 2), and N (4, 4)

It is also given that the triangle is then

transformed using the rule (x+5, y+2)

Let with the effect of transformation the point

( x , y) is transformed into ( x ', y ')

So that x = x' + h and y = y' + k

Which gives h = - 5 & k = - 2

By transformation ( x, y ) transformed into

( x + 5 , y + 2 )

FOR THE POINT L ( 2, 3 )

By transformation ( x, y ) transformed into

( x + 5 , y + 2 )

So the point L ( 2, 3 ) transformed into

L' ( 2 + 5 , 3 + 2 ) i.e L' ( 7 , 5 )

FOR THE POINT M ( 1 , 2 )

By transformation ( x, y ) transformed into

( x + 5 , y + 2 )

So the point M ( 1 , 2 ) transformed into

M' ( 1 + 5 , 2 + 2 ) i.e M' ( 6 , 4 )

FOR THE POINT N ( 4 , 4 )

By transformation ( x, y ) transformed into

( x + 5 , y + 2 )

So the point N ( 4 , 4 ) transformed into

N' ( 4 + 5 , 4 + 2 ) i.e N' ( 9 , 6 )

━━━━━━━━━━━━━━━━

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