find the value of m for which the points with coordinates (3,5),(m,6)&(1/2,15/2) are collinear.?

Answer 1

Since the three points are collinear, hence, the area of the triangle formed with these three points is zero. So apply any formula of calculating the area of triangle and equate it to zero.

Answer 2

Calculate the slope between points (3,5) and (1/2,15/2) and then find the point (m,6) that falls along that line.

Answer 3

let A(3,5) , B(m,6) and C(1/2,15/2) now if A,B,C are collinear then slope of AB = slope of AC. so eqating their slopes, we get,
(6-5)/(m-3) = (15/2-5)/(1/2-3)
1/m-3 = -1
1 = -m+3
m = 2

Answer 4

Find the equation of the line between (3, 5) and (1/2, 15/2):

(5-(15/2))/ (3-1/2) = (-5/2) / (5/2) = -1 for the slope

y = bx + c
5 = -1(3) + c
c = 8

Line : y = -x + 8
6 = -m + 8
-2 = -m
m = 2

Answer 5

Any two points determine the slope which does not change if the three points are collinear. Using the two points (4,0), (4, -3), the slope can be determined, which is undefined (vertical) It is clear now that k = 4

Answer 6

Slope is constant:
slope from end to 'm' point = slope between endpoints:
del_y / del_x :
(6-5)/(m-3) = (15/2-5)/(1/2-3) , solve for m...

Answer 7

3(6-15\2)+m(15\2-5)+1\2(5-6)=0
m=2.

Answer 8

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