McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
Standardized Test Practice

Exercise 4 Page 232

Let's put the three points on the coordinate plane and draw a line through the two given points. Next we draw a line through the third point that is perpendicular to line The distance of the point from the line can be measured along this perpendicular line.

Here is the plan we will follow to find the distance.

  1. We first find the equation of line
  2. Next we find the equation of the perpendicular line.
  3. Using the two equations, we can find the point of intersection.
  4. The distance of point and this intersection point is the distance of point from line

Let's now see the details.

Equation of Line

To find the equation of line we first use the Slope Formula to find its slope.
We can substitute the coordinates of the given points and , and simplify the expression to find the slope.
Simplify
We look for the equation in slope-intercept form.
We already know the slope, We can use a point on the line, to find the intercept
Solve for
We now have both the slope and the intercept to write the equation of the line through the points and

Equation of the Perpendicular Line

We again look for the equation in slope-intercept form. Since this line is perpendicular to line their slopes multiply to
We can use the slope of line which we found in the previous step, to find the slope of the perpendicular line.
Simplify
Knowing this slope we can use a point on the line, to find the intercept
Solve for
We now have both the slope and the intercept to write the equation of the line through the point that is perpendicular to

Intersection Point of the Lines

The diagram below shows the two lines and their equations.

To find the coordinates of the intersection point we solve the system of equations.
Solve for
We can use this value of and substitute it in the first equation to get the value of
Solve for
The point of intersection is

Distance of the Points

We need the distance of this point from We can use the Distance Formula.
Simplify

Answer

Since the two lines are perpendicular, the distance of from the point of intersection is the distance we are looking for.

The distance of from line is or about units. The correct answer choice is G.