A vertical line passes through the point $(-3,5)$. Which point is also on this line?

A. $(0,0)$
B. $(5,-3)$
C. $(-3,-4)$
D. $(-1,5)$

A vertical line passing through ( − 3 , 5 ) has the equation x = − 3 .
Check each point to see if its x -coordinate is − 3 .
The point ( − 3 , − 4 ) has an x -coordinate of − 3 .
Therefore, the point ( − 3 , − 4 ) is on the line. ( − 3 , − 4 ) ​

Explanation

Determine the equation of the vertical line. A vertical line is defined by the equation x = c , where c is a constant. Since the line passes through the point ( − 3 , 5 ) , the equation of the line is x = − 3 . We need to determine which of the given points also satisfies this equation.

Check each point. Let's check each point:

( 0 , 0 ) : The x -coordinate is 0 . Since 0 e q − 3 , this point is not on the line.

( 5 , − 3 ) : The x -coordinate is 5 . Since 5 e q − 3 , this point is not on the line.

( − 3 , − 4 ) : The x -coordinate is − 3 . Since − 3 = − 3 , this point is on the line.

( − 1 , 5 ) : The x -coordinate is − 1 . Since − 1 e q − 3 , this point is not on the line.

Conclusion. Therefore, the point ( − 3 , − 4 ) is on the vertical line x = − 3 .


Examples
Vertical lines are commonly encountered in coordinate geometry and have practical applications in various fields. For example, in architecture, vertical lines represent walls and support structures. In computer graphics, they can define boundaries or edges of objects. Understanding vertical lines helps in creating accurate representations and models in these fields.

Answered by GinnyAnswer | 2025-07-03

The only point that lies on the vertical line defined by x = − 3 is (-3, -4), making option C the correct choice. Other options do not satisfy the condition of having an x-coordinate of -3. Thus, the answer is C. (-3, -4).
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Answered by Anonymous | 2025-07-04