Question

In the graph below, find the coordinate of the image point. O is the origin and P is the point (4, 3). Ry and Rx are reflections around the x- and y- axes.
Complete the following:

Answer 1

Answer:

We have been given the points origin and P (4,3)

We have reflection rule which is:

$(x,y)\text{when reflected around y-axis}\Rightarrow(-x,y)$

$(x,y)\text{when reflected around x-axis}\Rightarrow(x,-y)$

The given point x=4 and y=3 when reflected around y-axis the point becomes:

(-4,3)

The given point x=4 and y=3 when reflected around x-axis the point becomes:

(4,-3)

Answer 2

Answer with explanation:

When a point is reflected across either through x or y axis ,then perpendicular distance of that point from x or y axis called Preimage is equal to perpendicular distance of that point from x or y axis called image.

When a point is reflected through x axis or y axis,it totally depends on which quadrant the point is lying.

If point(a,b) is lying in first Quadrant ,and then we have to find it's reflection across x axis and y axis then coordinate of image point will be ,which will lie in fourth Quadrant and second quadrant respectively ,will have coordinates  (a,-b) and (-a,b) respectively.

These are rules of reflection across x and y axis of point(a,b),where a and b are positive real number

$(a,b)_{x}=(a,-b)\\\\(a,b)_{y}=(-a,b)\\\\(-a,b)_{x}=(-a,-b)\\\\(-a,b)_{y}=(a,b)\\\\(-a,-b)_{x}=(-a,b)\\\\(-a,-b)_{y}=(a,-b)\\\\(a,-b)_{x}=(a,b)\\\\(a,-b)_{y}=(-a,-b)$

Using the Same rule when point (4,3) is reflected around x and y axes

$(4,3)_{x}=(4,-3)\\\\(4,3)_{y}=(-4,3)$