Question

hat is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6

Answer 1

Answer:

The point that divides the directed line segment from J to K into a ratio of 5:1 is (6, 0), its y-coordinate is 0.

Step-by-step explanation:

We take J as point one, with coordinates (x1, y1) = (1, -10) and K as point two with coordinates (x2, y2) = (7, 2)

The "run" is the change in the x-coordinates:  x2 - x1 = 7 - 1 = 6

The "rise" is the change in the y-coordinates: y2 - y1 = 2 - (-10) = 12

For the partition ratio, let the numerator = a and the denominator = b.

The coordinates of the point P (x, y), which divides the directed line segment from J to K into a ratio of 5:1 is:

x = x1 + a/(a+b)*run

x = 1 + 5/(5+1)*6

x = 6

y = y1 + a/(a+b)*rise

y = -10 + 5/(5+1)*12

y = 0