Find the value of p if the line joining the points (3, -6) and (p, 10) is perpendicular to the line 2x-5y=7.
Provide steps.
2006-09-16 08:02:12 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
perpendicular to 2x-5y=7
so slopewill be the negative inverse of the slope of this line
slope of this line=2/5
slope of the required line is -5/2
passes through (3,-6)
the equation is y-y1=m(x-x1)
y+6=-5/2(x-3)
cross multiplying
2y+12=-5x+15
5x-2y+3=0
point(p,10) lies on it and so it must satisfy the equation
5p-20+3=0
5p=17
p=17/5
2006-09-16 08:10:06 · answer #1 · answered by raj 7 · 0⤊ 0⤋
Find the slope of 2x-5y=7:
5y=2x-7
y=2/5x-7/5
M=2/5
Find the slope of the perpendicular line:
-1/M=-5/2
Find the slope of the line joining the indicated points:
(10+6)/(p-3)
Set this equal to the slope of the perpendicular line and solve:
(10+6)/(p-3)=-5/2
32/(p-3)=-5
32=-5p+15
-5p=17
p=-17/5
Note to rfamilymember:
2y+12=-5x+15 â 5x+2y-3=0, not 5x-2y+3=0
2006-09-16 08:11:37 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
reorganize 2x - 5y = 7
(2x - 7)/5 = y
y = 2/5 x - 7/5
slope = 2/5
A line perpendicular to this one has negative reciprocal slope so the slope is -5/2.
slope = delta Y / delta X = (10 - -6)/ (p - 3) = -5/2
16/(p-3) = -5/2
p-3 = -32/5
p = -17/5
2006-09-16 08:11:54 · answer #3 · answered by Scott S 2 · 0⤊ 0⤋
2x - 5y = 7
-5y = -2x + 7
y = (2/5)x - (7/5)
Perpendicular slope is (-5/2)
(3,-6) and (p,10)
m = (10 - (-6))/(p - 3)
m = (10 + 6)/(p - 3)
m = 16/(p - 3)
(-5/2) = (16/(p - 3))
-5(p - 3) = 32
-5p + 15 = 32
-5p = 17
p = (-17/5)
ANS : p = (-17/5)
2006-09-16 11:56:21 · answer #4 · answered by Sherman81 6 · 0⤊ 0⤋
The given line is,
2x-5y=7
or, y = (2/5)x-7/5, Slope of this line is m1 = 2/5
Now line joining (3,-6) and (p,10) has the slope,
m2 = (10-(-6))/(p-3), the formula is (y2-y1)/(x2-x1)
or, m2 = 16/(p-3)
Now two lines of slope m1 and m2 are said to be perpendicular if and only if,
m1*m2 = -1
So, we get, [2/5]*[16/(p-3)] = -1
or, -5p+15 = 32
or, p = - 17/5
Hope this helps.
2006-09-16 08:22:34 · answer #5 · answered by M1976 2 · 0⤊ 0⤋
Slope of given line is 2/5...................i
Slope of line joing two points is=(10+6)/(p-3)---------ii
since both are perpendicular, therefore
(2/5)X(10+6)/(p-3)=-1
32 = -5p+15
17 = -5p
p= - (17/5)
2006-09-16 08:19:39 · answer #6 · answered by Amar Soni 7 · 0⤊ 0⤋
pascal got it right.... p = -17/5
2006-09-16 08:21:55 · answer #7 · answered by m s 3 · 0⤊ 0⤋
Girl I cannot answer that question. I don't know algerbra.
2006-09-16 08:16:07 · answer #8 · answered by Anonymous · 0⤊ 1⤋