given R(-6,19) and S (14,-6), what are the coordinates of the oints on the segment RS two-fifths of the distance from R to S
(-6 , 19), P(X , Y), (14 , -6).
X - (-6)) = 2/5(14 - (-6)),
X + 6 = 2/5(14 + 6),
X + 6 = 2/5(20),
X + 6 = 8,
X = 8 - 6 = 2.
Y - 19 = 2/5(-6 - 19),
Y - 19 = 2/5(-25),
Y - 19 = -10,
Y = 19 - 10 = 9.
P(2 , 9).
To find the coordinates of the point that is two-fifths of the distance from R to S, we can use the midpoint formula. The midpoint formula gives us the coordinates of the point that lies exactly halfway between two given points.
The midpoint formula is:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using the given points:
R = (-6, 19)
S = (14, -6)
Let's calculate the midpoint:
Midpoint(x, y) = ((-6 + 14) / 2, (19 + -6) / 2)
= (8 / 2, 13 / 2)
= (4, 6.5)
Therefore, the coordinates of the point on the segment RS that is two-fifths of the distance from R to S are (4, 6.5).