Question

How do you determine the value of missing coordinates A $ \left( {0,d} \right) $ and B $ \left( {d,0} \right) $ if the slope is undefined ?

Answer 1

Hint: In the given question, we are provided with the coordinates of two points A and B. Now, we are also given that the slope of the line joining the two points given to us is undefined. We can also find the slope of the line joining the two points with the help of the coordinates of the two points. We know that a line having undefined slope is parallel to y axis. Hence, we can find the value of d and the missing coordinates.

Complete step by step solution:
In the given problem, the coordinates of the two points A and B provided to us are $ \left( {0,d} \right) $ and $ \left( {d,0} \right) $ .
Now, we know that a line that possesses undefined slope is parallel to y axis. Hence, the coordinates of the points must have the same x coordinate.
So, we get, $ d = 0 $ .
Hence, the value of d is zero.
Now, the coordinates of the point A are $ \left( {0,d} \right) = \left( {0,0} \right) $
The coordinates of the point A are $ \left( {d,0} \right) = \left( {0,0} \right) $
Hence, the missing coordinates of the points are A $ \left( {0,0} \right) $ and B $ \left( {0,0} \right) $ .
So, both point A and point B represent the same point on the coordinate plane, origin.
So, the correct answer is “(0,0)”.

Note: Slope of a line is the inclination of the straight line with the positive side of the x axis. It is also referred to as gradient of the line. It is calculated by the ratio of vertical change to horizontal change.