Given the point A(-3, -2) and B(6, 1), select two possible locations for point P so that P partitions AB in the ratio 2:1

Answer 1

the formula is:

(b x1 + a x2)/(a+b)

(b y1 + a y2) /(a+b)

x1=-3

x2=6

y1=-2

y2=1

a=2

b=1

(1*-3 + 2*6)/3 = (-3 + 12)/3 = 9/3 = 3

(1* -2 + 2 * 1)/3 = ( -2 + 2)/3 = 0

A(-3,-2) P(3,0) B(6,1)

check:

AP = sqrt( 6^2 + 2^2) = sqrt(36+4) = sqrt(40) = 2*sqrt(10)

PB = sqrt( 3^2 + 1^2) = sqrt(10)

AP/PB = 2/1

to find the other point, reverse the values of A and B, so

that the ratio is 1 to 2

x1=-3

x2=6

y1=-2

y2=1

a=1

b=2

and again for your convenience,

the formula is:

(b x1 + a x2)/(a+b) for the X coordinate of point P

(b y1 + a y2) /(a+b) for the Y coordinate of point P

(2 * -3 + 1 * 6)/3 = (-6+6)/3 = 0

(2* -2 + 1*1)/3 = (-4+1)/3 = -3/3 = -1

(0,-1)

A (-3,-2) P(0,-1) B(6,1)

AP = sqrt( 3^2 + 1^2) = sqrt(10)

PB = sqrt( 6^2 + 4^2) = sqrt(40) = 2*sqrt(10)

AP/PB = 1/2