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labwork [276]
3 years ago
7

line segment AB has endpoints A (7.5,4.2) and B (2.3,5.4). Find the coordinates of the point that divides the line segment direc

ted from A to B in the ratio of 1:3
Mathematics
1 answer:
Marrrta [24]3 years ago
5 0

9514 1404 393

Answer:

  (6.2, 4.5)

Step-by-step explanation:

We want, for some point P, ...

  (P -A) / (B -P) = 1 / 3

  3(P -A) = (B - P) . . . . . multiply by 3

  4P = B +3A . . . . . . . . add P+3A

  P = (B +3A)/4 . . . . . . .divide by 4

Filling in the coordinate values, we can find P to be ...

  P = ((2.3, 5.4) +3(7.5, 4.2))/4 = (2.3+22.5, 5.4+12.6)/4

  P = (6.2, 4.5)

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How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2. X 2 6x – 4y = –10 one
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The system of equations provides a unique solution(one solution) at (-0.6, 1.6).

<h2>Given to us,</h2>
  1. y=\dfrac{2}{3}x+2
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<h3>Equation 2</h3>

As we already have the value of y from equation 1, substitute its value in equation 2,

6x-4y=-10

6x-4(\dfrac{2}{3}x+2)=-10

6x-\dfrac{8}{3}x-8=-10

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x=\dfrac{-6}{10} \\\\x=-0.6

<h3>Equation 1,</h3>

y=\dfrac{2}{3}x+2

substitute the value of x in equation 1,

y=\dfrac{2}{3}(\dfrac{-6}{10})+2\\\\y = \dfrac{-2}{5}+2\\\\y= \dfrac{-2+10}{5}\\\\y = \dfrac{8}{5}\\\\y=1.6

As we can see the system of equations provides a unique solution(one solution) at (-0.6, 1.6).

Learn more about the system of equations:

brainly.com/question/12895249

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3 years ago
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