triangle ABC has vertices A(-3,10) B(9,2) C(9,15) Point P is the midpoint of segment AB and segment CP is a median of triangle ABC. The cordinates of point P is (3,6) Determine if segment CP is an altitude of triangle ABC.
P.S my teacher said you need to use the distance formula
2007-03-08 08:31:58 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Yes it is an altitude. What your teacher meant is the following:
Calculate:
Distance BC = Square Root of [(Xb-Xc)^2 + (Yb-Yc)^2] =13
Distance PB = Square Root of [(Xp-Xb)^2 + (Yp-Yb)^2]=10.82
Distance PC = Square Root of [(Xp-Xc)^2 + (Yb-Yc)^2]=7.21
Now check if Distance BC^2 = Distance PB^2+DistancePC^2
The answer is yes and the angle at point P is 90deg.
2007-03-08 08:42:13 · answer #1 · answered by Chad 1 · 0⤊ 0⤋
Wow, I notice alot of harsh answers today in the math section of answers! I'm guessing these people couldn't do the problem either.
I don't think the distance formula would be necessary to determine if it is an altitude. Now, once you know it is an altitude, then you could use the distance formula to find the length of it, which would be the height of your triangle.
To determine if it is an altitude, CP must intersect AB at a 90 degree angle. My instinct is to find the slope of line AB and find the slope of line CP. If they are negative reciprocals of one another, then they are perpendicular lines and so intersect at a 90 degree angle. Or if, when you mulitply the slopes together, the product equals -1, that also would mean they are perpendicular lines.
If they are perpendicular lines, this means they intersect at 90 degrees, and this would make CP an altitude. Then, use the distance formula to find the altitude.
Hope this helps.
2007-03-08 08:38:43 · answer #2 · answered by vidigod 3 · 0⤊ 0⤋
The slope of the line CP is (15-6)/(9-3) = 9/6 = 3/2.
The slope of the line AB is (2-10)/ (9-(-3)) = -8/12= -2/3
Since the slopes of these two lines are negative reciprocals of each other, the two lines are perpendicular to each other. Therefore the CP is also an altitude of triangle ABC.
Your teacher is incorrect. There is no need to use the distance formula, nor would it do you any good.
(3/2)(-2/3) = -1 indicates lines are perpendicular.
2007-03-08 08:47:28 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
Yes CP is an altitude
2007-03-08 08:36:36 · answer #4 · answered by Catman 4 · 0⤊ 1⤋
listen to the freaking teacher when she is talking and you wont have to ask us to help you with your homework
2007-03-08 08:35:08 · answer #5 · answered by Anonymous · 0⤊ 2⤋