On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 8, negative 13) and point B is at (4, 11). What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is One-third the length of the line segment from A to B? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 (1, 5) (0, 3) (–4, –5) (–5, –7)
Answers
Given : On a coordinate plane, a line is drawn from point A to point B . A (-8 , -13) , B ( 4 , 11) . P on the directed line segment from A to B such that P is One-third the length of the line segment from A to B
To find : Coordinate of P
Solution:
A (-8 , -13)
B ( 4 , 11)
coordinates of point P ( x , y)
AP = AB/3
BP = AB - AP = AB - AB/3 = 2AB/3
=> AP : BP = 1 : 2
point P divides line segment AB into 1 : 2 ratio
x = ( 1 * 4 + 2*(-8))/(1 + 2) = -12/3 = -4
y = ( 1 * 11 + 2*(-13))/(1 + 2) = -15/3 = -5
P = (-4 , - 5)
(-4 , - 5) is the correct option
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