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At what point the origin be shifted, if the coordinates of a point $(-1,8)$ becomes $(-7,3)$.

Let origin be shifted by $(h,k)$. so we have

$-1=-7+h$

$8=3+k$

solving i get $(h,k)=(6,5)$. But textbook states answer to be $(-6,-5)$. i am thoroughly confused

3 Answers 3

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You are doing it backwards, so you get the opposite answer. $(-1,8)$ becomes $(-7,3)$ so you are shifting $(-1,8) \to (-7,3).$ So $$ -1+h = -7 \\ 8+k = 3.$$

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    formula is $x=X+h$ , – 2017-02-11
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    @Gathdi If $-1$ becomes $-7$ what does $0$ become? – 2017-02-11
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    okay got it thanks – 2017-02-12
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All points get the same shift, so:

if $(−1,8)+(h,k)=(−7,3)$,

then the shift is $(h,k)=(−7,3)-(−1,8)=(−6,−5)$

Because the shift is the same for all points, then is the same for the origin.

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Let $(x,y) = (-1,8)$ be the original point, and $(x',y') = (-7,3)$ the shifted point.

Shift:

$P(x,y)$ $ \rightarrow $ $P'(x',y')$, where

$1) x $$ \rightarrow$ $x' = x + a$;

$2) y $$ \rightarrow$ $ y' = y + b$.

As row vectors:

$(x',y') = (x,y) + (a,b)$.

Now calculate $a$ and $b$:

$1) - 7 = - 1 + a$,

$ a = - 6$;

$2) 3 = 8 + b$,

$b= - 5$.

Shift of origin $O$ $\rightarrow$ $O'$ :

$(x',y') = (0,0) + (-6,-5) = (-6,-5)$.