Concept explainers
Find the point on the line that is closest to the point .
To calculate: The point on the line that is closest to the point .
Answer to Problem 88AYU
The point that is closest to the point is .
Explanation of Solution
Given:
The given line is .
Formula used:
The distance formula between 2 points and is
Consider a quadratic function of the form .
Then the graph of the above function is a parabola with vertex .
This vertex is the highest point if and the lowest point if .
Therefore, the maximum (or the minimum) value of the function will be .
Calculation:
Here, we have .
Therefore, the distance between the points and is
Now, we know the equation . Therefore, we can substitute for in the above equation as
Now, let
Therefore, we have
Here, we have ; therefore, the function is having a minimum value at its vertex.
Therefore, we get
.
.
Thus, we get the vertex of the function as , which is the minimum value of the distance function.
Therefore, we can say that is the point that is closest to the point .
Chapter 3 Solutions
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