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# Find the image of point $\left( 1,7 \right)$ in x-axis and y-axis.

Last updated date: 15th Jul 2024
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Two numbers that represent a point on a graph, are also called the coordinates. Abscissa - The horizontal line, or x-axis, of a graph. Ordinate - The vertical line, or y-axis, of a graph. Origin - The origin is the point where the X and Y axis intersect on a graph. This is the point $\left( 0,0 \right)$ in a two-dimensional graph. The x-coordinate of a point is the value that tells you how far from the origin the point is on the horizontal, or x-axis. The y-coordinate of a point is the value that tells you how far from the origin the point is on the vertical, or y-axis.
To find the coordinates, the x-axis represents the plain mirror. M is the point in the rectangular axes in the first quadrant whose coordinates are $\left( h,k \right)$ . When point M is reflected in the x-axis, the image M’ is formed in the fourth quadrant whose coordinates are $\left( h,-k \right)$ . Thus, we conclude that when a point is reflected in the x-axis, then the x-co-ordinate remains the same, but the y-coordinate becomes negative. Thus, the image of point $M\left( h,k \right)$ is $M'\left( h,-k \right)$ . Thus, the reflection of the point $\left( 1,7 \right)$ , lying in the first quadrant, in the x-axis will be $\left( 1,-7 \right)$ .
To find the coordinates, the y-axis represents the plain mirror. N is the point in the rectangular axes in the first quadrant whose coordinates are $\left( h,k \right)$ . When point N is reflected in the y-axis, the image N’ is formed in the second quadrant whose coordinates are $\left( -h,k \right)$ . Thus, we conclude that when a point is reflected in the y-axis, then the y-coordinate remains the same, but the x-co-ordinate becomes negative. Thus, the image of point $N\left( h,k \right)$ is $N'\left( -h,k \right)$ . Thus, the reflection of the point $\left( 1,7 \right)$ , lying in the first quadrant, in the y-axis will be $\left( -1,7 \right)$ .
Hence, the image of the point $\left( 1,7 \right)$ after being reflected in the x and y axes respectively are $\left( -1,-7 \right)$ and $\left( -1,7 \right)$ .