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ivolga24 [154]
3 years ago
11

the coordinates of the endpoints of AB are A (-8, -2) and B(16,6). Point P is on AB what are the coordinates of point P such tha

t AP:PB is 3:5?

Mathematics
1 answer:
garri49 [273]3 years ago
6 0
We have that
<span>A (-8, -2) and B(16,6)

step 1
find the distance AB in the x coordinates
dABx=(16-(-8))-----> 24 units

step 2
find coordinate x of P (Px)
Px=Ax+(3/5)*dABx------> Px=(-8)+(3/5)*24----> 6.4

step 3
F</span>ind the distance AB in the y coordinates
dABy=(6-(-2))-----> 8 units

step 4
find coordinate y of P (Py)
Py=Ay+(3/5)*dABy------> Py=(-2)+(3/5)*8----> 2.8

the coordinates of P are (6.4,2.8)

see the attached figure

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\boxed{x=1, \y=-1, \ z=2}

<h2>Step-by-step explanation:</h2>

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Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}

Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}

Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}

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\frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}

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x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}

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