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MAXImum [283]
3 years ago
5

Directed line segment has endpoints P(– 8, – 4) and Q(4, 12). Determine the point that partitions the directed line segment in a

ratio of 3:1.
Mathematics
1 answer:
larisa86 [58]3 years ago
7 0

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

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

Let us substitute coordinates of point P and Q as:

x_1=-8,

y_1=-4

x_2=4

y_2=12

m=3

n=1

[x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}]

[x=\frac{12-8}{4},y=\frac{36-4}{4}]

[x=\frac{4}{4},y=\frac{32}{4}]

[x=1,y=8]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

   

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