Mathematics: Segment rs has endpoints at r(5,-3) and s(5,13) , point q lies on rs such that rq : qs = 3 : 1 . which of the following must be on the coordinates of q? (1) (5,1) (2) (17,3) (3) (5,9) (4) (6,4)

Segment rs has endpoints at r(5,-3) and s(5,13)

Ответ:

glyptictriton9575

15.01.2022

Mathematics

(3) Q(5,9)

Step-by-step explanation:

Let point Q has coordinates (x,y). Consider vectors $\overrightarrow{RQ}$ and $\overrightarrow{QS}.$ Note that

$\overrightarrow{RQ}=(x-5,y+3);$ $\overrightarrow{QS}=(5-x,13-y).$

Since $\dfrac{RQ}{QS}=\dfrac{3}{1},$ then

$\dfrac{\overrightarrow{RQ}}{\overrightarrow{QS}}=\dfrac{3}{1},$

Thus,

$\dfrac{x-5}{5-x}=\dfrac{3}{1}\Rightarrow x-5=3(5-x),\ x-5=15-3x,\ 4x=20,\ x=5.\\ \\\dfrac{y+3}{13-y}=\dfrac{3}{1}\Rightarrow y+3=3(13-y),\ y+3=39-3y,\ 4y=36,\ y=9.$

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Ответ:

Theacefamily123

25.02.2020

Mathematics

Adjacent AnglesTwo angles areAdjacent if they have a common side and a common vertex. ... VerticalAnglesVertical Angles are the anglesopposite each other when two lines cross.They are called "Vertical" because they share the same Vertex.Vertical Angles are Congruent/equivalent

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Segment rs has endpoints at r(5,-3) and s(5,13) , point q lies on rs such that rq : qs = 3 : 1 . which of the following must be on the coordinates of q?
(1) (5,1)
(2) (17,3)
(3) (5,9)
(4) (6,4)

Ответ:

Ответ:

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