Find the coordinates of a point on the directed segment from (3,-2) to (8,0) that divides into a ratio of 3: 1.
a. (6.75, -0.5)
b. (6, -.075)
c. (5, -1.5)
d. (4, -1.5)

  (x, y) = (6.75, -0.5)

Step-by-step explanation:

You require the point (x, y) such that the distance from (3, -2) is 3 times the distance from (8, 0). That is ...

  x-3 = 3(8 -x)

and

  y-(-2) = 3(0 -y)

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Solving the first equation, we get ...

  x -3 = 24 -3x

  4x = 27 . . . . . . . . . . . . add 3x+3

  x = 27/4 = 6.75 . . . . . . this is sufficient to choose the correct answer.

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Solving the second equation, we get ...

  y +2 = -3y

  4y +2 = 0 . . . . . add 3y

  y + 1/2 = 0 . . . . . divide by 4

  y = -0.5 . . . . . . . . . . . this confirms the correct answer choice.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.

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