SOLUTION: Sue wants to form a right angle to create a right triangular garden and decides to make a blueprint of the right angle . AB has the equation: y= 2x+1 AC has the equation x=4

Question 1112872: Sue wants to form a right angle to create a right triangular garden and decides to make a blueprint of the right angle .
AB has the equation: y= 2x+1
AC has the equation x=4
BC is perpendicular to AB passing through the point (-8,0)
Graph all three equation on a single graph
What is the soulution of AB and BC on the graph label it B
Prove the solution you got for the intersection of AB and BC was correct by solving the system of equations algebrically
Find the perimeter of the right triangle garden

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The slopes of perpendicular lines are negative reciprocals. Since the slope of the line containing the segment AB is 2, the slope of the perpendicular line containing the segment BC must be

Using the Point-Slope form, a line with a slope of

passing through the point

is given by:

Or simplified to Slope-Intercept form:

The equation of the line containing the segment AB is given in slope-intercept form, so just equate the two right-hand sides:

Solve for

and then substitute back into either equation to find

, then verify that the point of intersection is indeed

.

Substitute

into both equations to find the coordinates of the other two points.

Then use the distance formula:

Three times giving you the lengths of the three sides. Add the measures of the three sides to get the perimeter. Leave your answer in radical form to express the answer exactly.

John

My calculator said it, I believe it, that settles it

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