Question

If origin is shifted to (3, 1) then new equation of line x + y = 4 is

Answer 1

Step-by-step explanation:

(x−3)

2

+(y+4)

2

=4

x

2

−6x+9+y

2

+8y+16=4

x

2

+y

2

−6x+8y+25−4=0

⇒x

2

+y

2

−6x+8y

Answer 2

SOLUTION

TO DETERMINE

If origin is shifted to (3, 1) then new equation of line x + y = 4 is

CONCEPT TO BE IMPLEMENTED

If the origin is shifted to (h, k) so that the point (x, y) in old coordinate system is transformed into (x', y')

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

EVALUATION

Here the given equation of the line is

x + y = 4

Now the origin is shifted to (3, 1) so that the point (x, y) in old coordinate system is transformed into (x', y')

Then x = x' + 3 and y = y' + 1

From Equation 1 we get

$\sf \: x + y = 4$

$\displaystyle \sf{ \implies (x' + 3) + (y' + 1) = 4}$

$\displaystyle \sf{ \implies x' + y' + 4 = 4}$

$\displaystyle \sf{ \implies x' + y' =0}$

Which is the required equation of the line

FINAL ANSWER

If origin is shifted to (3, 1) then new equation of line x + y = 4 is x' + y' = 0

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