three points P Q and R have co-ordinates (2,1) , (4,7) and (1,b) respectively.
Find b if
1) QR is perpendicular to PQ
2)QPR is a straight line
plz help me..thanx:D
2007-01-17 08:09:35 · 3 answers · asked by thelittle_angel1327 2 in Science & Mathematics ➔ Mathematics
1) the property of perpendicular is that the two lines will their slope reciprocal to one another. So,
slope for PQ is (7-1)/(4-2) = 3. Therefore, we know that the slope for QR is -1/3. And
slope of QR is -1/3 = (b-7)/(1-4), and solving for b, we get,
b= 8 Ans.
2) If QPR is a straight line, and slope of PR is 3; so, we know that QPR will have a slope of 3 also. Just pick any point P or Q and point R to solve for b. Let's pick P & R
Slope:
3 = (b-7)/(1-4), in solving for b, we get:
b = -2 Ans.
2007-01-17 08:22:14 · answer #1 · answered by Cu Den 2 · 0⤊ 0⤋
If perpendicular, the slopes have to be negative reciprocals.
mPQ = (7 - 1) /(4 - 2) = 6/2 = 3
Therefore m QR must be -1/3.
mQR = (b - 7)/(1 - 4)
-1/3 = (b - 7)/(-3)
1 = b - 7
8 = b
If they are collinear it means they have equal slopes.
mQR = 3
3 = (b-1)/-3
-9 = b - 1
-8 = b
2007-01-17 16:16:11 · answer #2 · answered by keely_66 3 · 0⤊ 1⤋
1) b=8
2) b=(-2)
2007-01-17 16:14:57 · answer #3 · answered by Veer 3 · 0⤊ 0⤋