Concept explainers
Construct a line perpendicular to l through P(1,7). Find the distance from P to l .
Answer to Problem 2CYP
Explanation of Solution
Given :
Line l contains points at (1,2) and (5,4) .
Formula Used:
Distance between a point and a line :
The distance between a line and a point not on the line is the length of the segment perpendicular to the line from the point.
Calculation :
Draw the line l and a line
First , find the equations of line l and
By
Now, the equation of line l is :
The product of slopes of two perpendicular lines is -1 .
So, slope of the line
It passes through the point (1,7) , so the equation of
Now , we find the point of intersection of line l and
Multiply equation (1) by 2 and add:
Substitute in equation (1) and solve for x :
So, the two lines intersect at Q(3,3)
Now, the distance from P to l is the distance between the points P(1,7) and Q(3,3) :
Chapter 3 Solutions
Geometry, Student Edition
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