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snow_tiger [21]
3 years ago
6

What are the coordinates of point P on a directed line segment from R to Q such that P is 5/6 the length of the line segment.

Mathematics
1 answer:
Black_prince [1.1K]3 years ago
7 0

Answer:

P = [-3/5,2.33]

Step-by-step explanation:

Given

See attachment for line segment RQ

P = \frac{5}{6} of RQ

Required

The coordinates of P

Using line segment ratio formula, we have:

P = [\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n}]

If P is at:

P = \frac{5}{6}

Then:

m : n = \frac{5}{6} :  1 -\frac{5}{6}

Solve

m : n = \frac{5}{6} :  \frac{6-5}{6}

m : n = \frac{5}{6} :  \frac{1}{6}

Multiply by 6

m : n = \frac{5}{6} *6:  \frac{1}{6} * 6

m : n = 5 : 1

By comparison

m=5\ \& n = 1

From the attached line segment

R(x_1,y_1) = (4,-1)

Q(x_2,y_2) = (-5,3)

So, we have:

P = [\frac{5*-5 + 1*4}{5+1},\frac{5*3 + 1*-1}{5+1}]

P = [\frac{-25 + 4}{6},\frac{15 -1}{6}]

P = [\frac{-21}{6},\frac{14}{6}]

P = [-3/5,2.33]

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Pick one of the coordinates, I’ll use (-3,-4) as the example.

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