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

The image of point P after reflecting it over the y-axis is (-4, 3). Then, reflecting it over the x-axis gives (-4, -3). Therefore, the answer is (-4, -3).

A reflection across the x-axis flips a point over the x-axis, negating its y-coordinate.

A reflection across the y-axis flips a point over the y-axis, negating its x-coordinate.

To reflect point P(4, 3) across the x-axis, we negate its y-coordinate, giving us the point P'(4, -3).

To reflect point P'(4, -3) across the y-axis, we negate its x-coordinate, giving us the point P''(-4, -3).

To reflect point P''(-4, -3) across the x-axis, we negate its y-coordinate, giving us the point P'''(-4, 3).

Therefore, the coordinate of the image point is (-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)`