Question

the coordinates of the image if the point -4,5 in y axis are
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Answer 1

To find: the coordinates of the image if the point is $(-4,5)$.

Solution:

Draw the required graph.

Observe that the image of the point $(-4,5)$ is $(-4,-5)$.

Answer 2

Given:

A point (-4, 5) lying in the 2D coordinate system.

To Find:

The image of the point (-4, 5) to the y axis.

Solution:

The given problem can be solved by using the concepts of 2D coordinate geometry.

1. The given point is (-4, 5).

• Consider a point P(x, y) in a 2D coordinate system. The point P(x, y) lies at a distance of x units from the y-axis and y units from the x-axis.
• The image of the point P(x, y) to the x-axis is at a vertical distance of x units from the x-axis on the opposite side of the original point.

Example: If the point P(x,y) lies in the first quadrant then, the image of the point P(x,y) to the x-axis is P(x,-y).

• The image of the point P(x, y) to the y-axis is at a vertical distance of y units from the y-axis on the opposite side of the original point.

Example: If the point P(x,y) lies in the first quadrant then, the image of the point P(x,y) to the y-axis is P(-x,y).

2. Hence from the mentioned properties above, we can find the coordinates of the image of the point (-4,5).

• The image of (-4,5) to the y-axis is at a  vertical distance of 4 units from the y-axis on the opposite side.

3. Hence the image of the point is (4,5).

Therefore, the image of the point (-4,5) in y-axis is (4,5).