Question

The image of a point is given by the rule ry = –x(x, y) → (–4, 9). What are the coordinates of its pre-image?

Answer 1

Answer:

The coordinates of pre-image are (-9,4).

Step-by-step explanation:

The image of a point is given by the rule

$R_{y=-x}(x,y)\rightarrow (-4,9)$         ..... (1)

It means the point is reflected about the line y=-x.

Let the coordinates of its pre-image are (x,y).

If a point reflected about the line y=-x, then

$(x,y)\rightarrow (-y,-x)$                   .... (2)

Compare the image points.

$(-y,-x)=(-4,9)$

On comparing both the sides we get,

$-y=-4\Rightarrow y=4$

$-x=9\Rightarrow x=-9$

Therefore the coordinates of pre-image are (-9,4).

Answer 2

The coordinates of its pre-image = A (-9.4)

Further explanation

Transformation is a change in shape or change in location from a building to another build.

A build can be changed in shape or location using transformation

There are several forms of transformation, including translation, dilation, rotation or reflection.

Reflection from a point or shape is a reflection of a point or shape to a certain line called the mirror axis

A point A (x, y) is reflected on the line y = -x so that the shadow of point

A '(x', y ') is obtained. The relationship between these two points is determined by:

x '= -y

y '= -x

A (x, y) --- (y = -x )---> A '(- y, -x)

y = –x (x, y) --> (–4, 9).

A shadow of point A '(- 4.9) which is reflected by the line y = -x, the starting point of the relation formula above is:

x '= -y

-4 = -y

4 = y

and

y '= -x

9 = -x

-9 = x

So the starting point = A (-9.4)

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Keywords: transformation, translation, dilation, rotation reflection