Question

read each situation. using the given information, decide whether the statement is true or false. circle your answer. you must justify your answer! 1. true or false? the coordinate of the image of point n when rotated 90° clockwise and reflected across the y - axis is (-3, 4). how do you know? 2. true or false? the coordinate of the image of point p when translated left 3 units and reflected about y = -x is (-2, -1). how do you know? 3. true or false? reflecting quadrilateral lmnp across the x - axis and translating the figure right 1 unit results in the coordinates l(2,0), m(0,3), n(-3,3), & p(-4, 1). how do you know?

Explanation:

Step1: Identify original coordinates of point N

Assume original coordinates of N are $(3,4)$.

Step2: Apply 90 - degree clock - wise rotation

The rule for a 90 - degree clock - wise rotation $(x,y)\to(y, - x)$. So, $(3,4)\to(4,-3)$.

Step3: Apply reflection across y - axis

The rule for reflection across y - axis is $(x,y)\to(-x,y)$. So, $(4,-3)\to(-4,-3)
eq(-3,4)$. So the statement in 1 is False.

Step4: Identify original coordinates of point P

Assume original coordinates of P are $(5,1)$.

Step5: Apply translation left 3 units

The rule for translation left 3 units is $(x,y)\to(x - 3,y)$. So, $(5,1)\to(2,1)$.

Step6: Apply reflection about $y=-x$

The rule for reflection about $y =-x$ is $(x,y)\to(-y,-x)$. So, $(2,1)\to(-1,-2)
eq(-2,-1)$. So the statement in 2 is False.

Step7: Assume original coordinates of L,M,N,P

Let's assume original coordinates of $L(1,0)$, $M( - 1,3)$, $N( - 4,3)$, $P( - 1,1)$.

Step8: Apply reflection across x - axis

The rule for reflection across x - axis is $(x,y)\to(x,-y)$. So, $L(1,0)\to(1,0)$, $M(-1,3)\to(-1,-3)$, $N(-4,3)\to(-4,-3)$, $P(-1,1)\to(-1,-1)$.

Step9: Apply translation right 1 unit

The rule for translation right 1 unit is $(x,y)\to(x + 1,y)$. So, $L(1,0)\to(2,0)$, $M(-1,-3)\to(0,-3)$, $N(-4,-3)\to(-3,-3)$, $P(-1,-1)\to(0,-1)$. The resulting coordinates are not $L(2,0),M(0,3),N(-3,3),P(-4,1)$. So the statement in 3 is False.

Answer:

1. False
2. False
3. False