Where would we find the point $(-10,0)$?
A) $x$-axis
B) $y$-axis
C) Quadrant III
D) Quadrant II
Answer (2)
The point ( − 10 , 0 ) has a y -coordinate of 0.
Points with a y -coordinate of 0 lie on the x -axis.
The x -coordinate is − 10 , indicating a location 10 units to the left of the origin.
Therefore, the point ( − 10 , 0 ) is on the x -axis: x -axis .
Explanation
Analyze the options The point in question is ( − 10 , 0 ) . We need to determine where this point is located on the coordinate plane. Let's analyze the options:
A) x -axis: The x -axis is the horizontal line where all points have a y -coordinate of 0. So, any point of the form ( x , 0 ) lies on the x -axis. B) y -axis: The y -axis is the vertical line where all points have an x -coordinate of 0. So, any point of the form ( 0 , y ) lies on the y -axis. C) Quadrant III: In Quadrant III, both the x and y coordinates are negative. So, any point in Quadrant III has the form ( − x , − y ) where 0"> x > 0 and 0"> y > 0 .
D) Quadrant II: In Quadrant II, the x -coordinate is negative and the y -coordinate is positive. So, any point in Quadrant II has the form ( − x , y ) where 0"> x > 0 and 0"> y > 0 .
Determine the location of the point Since the point ( − 10 , 0 ) has a y -coordinate of 0, it must lie on the x -axis. The x -coordinate is − 10 , which means it is located 10 units to the left of the origin (0, 0) on the x -axis.
Final Answer Therefore, the point ( − 10 , 0 ) is located on the x -axis.
Examples
Understanding coordinate systems is crucial in many real-world applications. For example, in GPS navigation, locations are defined using coordinates. Similarly, in computer graphics and video games, objects are positioned using coordinate systems. Knowing where a point lies on a coordinate plane helps in mapping, spatial reasoning, and understanding relationships between different locations or objects.
The point ( − 10 , 0 ) is located on the x -axis because it has a y -coordinate of 0, which defines the horizontal axis. The x -coordinate of − 10 indicates it is positioned 10 units to the left of the origin. Therefore, the chosen option is A) x -axis.
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