Graph rectangle MNOP with vertices M(-2,6),N(2,8),O(5,2) and P(1,0) and reflect it across the following lines of reflection: 1) x=0 2) y=3 3) y=x 4) y=-x

Question

Pergunta

Graph rectangle MNOP with vertices M(-2,6),N(2,8),O(5,2) and P(1,0) and reflect it across the following lines of reflection: 1) x=0 2) y=3 3) y=x 4) y=-x

Answer 1

To reflect the rectangle MNOP across the given lines of reflection, we need to find the coordinates of the reflected points. 1) Reflection across the line $x=0$: The line $x=0$ is the y-axis. To reflect a point across the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same. So, the reflected points are: $M'(-2,6) \rightarrow M'(2,6)$ $N(2,8) \rightarrow N'(-2,8)$ $O(5,2) \rightarrow O'(-5,2)$ $P(1,0) \rightarrow P'(-1,0)$ 2) Reflection across the line $y=3$: The line $y=3$ is a horizontal line. To reflect a point across a horizontal line, we change the y-coordinate to $2y_{line}-y$, where $y_{line}$ is the y-coordinate of the line of reflection. So, the reflected points are: $M(-2,6) \rightarrow M'(-2,6)$ $N(2,8) \rightarrow N'(2,2)$ $O(5,2) \rightarrow O'(5,4)$ $P(1,0) \rightarrow P'(1,6)$ 3) Reflection across the line $y=x$: The line $y=x$ is a diagonal line. To reflect a point across the line=x$, we swap the x-coordinate and y-coordinate of the point. So, the reflected points are: $M(-2,6) \rightarrow M'(6,-2)$ $N(2,8) \rightarrow N'(8,2)$ $O(5,2) \rightarrow O'(2,5)$ $P(1,0) \rightarrow P'(0,1)$ 4) Reflection across the line $y=-x$: The line $y=-x$ is also a diagonal line. To reflect a point across the line $y=-x$, we swap the x-coordinate and y-coordinate of the point and change their signs. So, the reflected points are: $M(-2,6) \rightarrow M'(-6,2)$ $N(2,8) \rightarrow N'(-2$O(5,2) \rightarrow O'(-2,5)$ $P(1,0) \rightarrow P'(0,-1)$ Therefore, the reflected rectangle MNOP across the given lines of reflection are: 1) $M'(2,6), N'(-2,8), O'(-5,2), P'(-1,0)$ 2) $M'(-2,6), N'(2,2),5,4), P'(1,6)$ 3) $M'(6,-2), N'(8,2), O'(2,5), P'(0,1)$ 4) $M'(-6,2), N'(-8,2), O'(-2,5), P'(0,-1)$

Pergunta

Graph rectangle MNOP with vertices M(-2,6),N(2,8),O(5,2) and P(1,0) and reflect it across the following lines of reflection: 1) x=0 2) y=3 3) y=x 4) y=-x

Solução

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