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: Â 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
Lines can be divided into different segments of different lengths using ratios.
The y-coordinate of the point at this ratio is 0
The coordinates of J and K are given as:
[tex]\mathbf{J = (1,-10)}[/tex]
[tex]\mathbf{K = (7,2)}[/tex]
The ratio is given as:
[tex]\mathbf{m:n =5:1}[/tex]
The y-coordinate of the point at this ratio is calculated using:
[tex]\mathbf{y_p = \frac{my_2 + ny_1}{m+n}}[/tex]
So, we have:
[tex]\mathbf{y_p = \frac{5 \times 2 + 1 \times -10}{5+1}}[/tex]
[tex]\mathbf{y_p = \frac{10 -10}{5+1}}[/tex]
Simplify the numerator, and the denominator
[tex]\mathbf{y_p = \frac{0}{6}}[/tex]
Divide the fraction
[tex]\mathbf{y_p = 0}[/tex]
Hence, the y-coordinate is 0
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