If the reflection of a point A(2,3) in the X- | vedclass

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(D) The reflection of a point $(x, y)$ about the $X$-axis is $(x, -y)$.Therefore,the coordinates of $B$ are $(2, -3)$.The reflection of a point $(x, y

Vedclass · Accepted Answer

$(2,-1)$

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(D) The reflection of a point $(x, y)$ about the $X$-axis is $(x, -y)$.Therefore,the coordinates of $B$ are $(2, -3)$.The reflection of a point $(x, y)$ about the line $x+y=0$ is $(-y, -x)$.Therefore,the coordinates of $C$ are $(-(-3), -(2)) = (3, -2)$.The reflection of a point $(x, y)$ about the line $x-y=0$ is $(y, x)$.Therefore,the coordinates of $D$ are $(-2, 3)$.The line $AB$ passes through $(2, 3)$ and $(2, -3)$,so its equation is $x=2$.The line $CD$ passes through $(3, -2)$ and $(-2, 3)$. The slope $m = \frac{3 - (-2)}{-2 - 3} = \frac{5}{-5} = -1$.The equation of $CD$ is $y - 3 = -1(x + 2)$ $\Rightarrow y - 3 = -x - 2$ $\Rightarrow x + y = 1$.Substituting $x=2$ into $x+y=1$,we get $2+y=1 \Rightarrow y=-1$.Thus,the point of intersection is $(2, -1)$.

If the reflection of a point $A(2,3)$ in the $X$-axis is $B$; the reflection of $B$ in the line $x+y=0$ is $C$,and the reflection of $C$ in $x-y=0$ is $D$,then the point of intersection of the lines $CD$ and $AB$ is:

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