SOLUTION: http://i.imgur.com/XGZpcvN.jpg In the figure above. AB=12. AC=15. and CD=6. Both AB and CD are perpendicular to AC. If the area of triangle ABE is p and the area of triangle CDE is

Question 1043743: http://i.imgur.com/XGZpcvN.jpg In the figure above. AB=12. AC=15. and CD=6. Both AB and CD are perpendicular to AC. If the area of triangle ABE is p and the area of triangle CDE is q, then what is the value of p-q?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we are going to determine the equations of AD and BC, this will allow us to determine the altitudes of triangles ABE and CDE
:
locate the vertex at the origin (0,0) then the figure is in quadrant 1 (x>0, y>0)
:
slope of AD = 6/15 = 2/5 and equation of AD is y = 2x/5
:
slope of BC = 12/-15 = -4/5 and equation of BC is y = -4x/5 + 12
:
The coordinates for point E is determined by setting the above equations = to each other
:
2x/5 = -4x/5 + 12
:
2x = -4x + 60
:
x = 10 then
y = 2(10)/5 = 4
:
point E is located at (10,4)
:
we can use the formula for the perpendicular distance from a point to a line
:
d = |Am + Bn +C| / square root(A^2 + B^2) where (m,n) is the point (10,4) and
:
Ax +By + C = 0
:
consider line segment AB, its equation is x = 0
:
d for E to AB = 10
:
p = (1/2) * 12 * 10 = 60
:
consider line segment CD, its equation is x -15 = 0
:
d for E to CD = 5
:
q = (1/2) * 5 * 6 = 15
:
********************
p - q = 60 - 15 = 45
********************
:

RELATED QUESTIONS
In the figure, ACB is an arc of a circle, and CD is the perpendicular bisector of chord... (answered by ikleyn)

In triangle ABC, AB = 9, BC = 12, AC = 15, and CD is the angle bisector. Find the length... (answered by ikleyn,addingup)

In the figure AB = AC = CD and AB = AB. Find the measure of angle ADC in degrees. (answered by ikleyn)

IN THE GIVEN FIGURE AC MEETS CD AND AB AT POINT C AND A RESPECTIVELY,SUCH THAT... (answered by tommyt3rd)

. In the figure, AB= AC and BC= CD. Find the marked angles. B=65° (answered by solver91311)

In quadrilateral ABCD, AB is congruent to CD, AB is parallel to CD, and BF and DE are... (answered by ikleyn)

We are learning about similar triangles (AA, SSS & SAS) and I am stuck on the following... (answered by scott8148)

i the circle, AB is parallel to CD and AB is a diameter. If AB=20 and CD= 2 root 51, how (answered by toidayma)

Assume that DABC below is an equilateral triangle. If CD^(perpendicular) AB and CD = 6,... (answered by Edwin McCravy)