Chandler200417idn
Answered

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Find the coordinates of P so that P partitions segment A to B in the ratio 5:1 with A(2,
4) and B(8, 10).

Find The Coordinates Of P So That P Partitions Segment A To B In The Ratio 51 With A2 4 And B8 10 class=

Sagot :

Elcharly64idn

Answer:

Point P has coordinates (7,9) (last choice)

Step-by-step explanation:

We are given the endpoints A(2,4) B(8,10) and the point P lying on the segment AB with the condition that P partitions it in the ratio 5:1.

This means the distances AP, PB and AB follow the conditions:

[tex]\frac{AP}{PB}=\frac{5}{1}[/tex]

AP+PB=AB

We can work with each coordinate separately. Suppose P has coordinates (x,y), thus:

[tex]x-x_a=5(x_b-x)[/tex]

[tex]x-x_a=5x_b-5x[/tex]

Adding 5x and subtracting:

[tex]6x=5x_b+x_a[/tex]

Dividing by 6:

[tex]\displaystyle x=\frac{5x_b+x_a}{6}[/tex]

Substituting:

[tex]\displaystyle x=\frac{5*8+2}{6}=\frac{42}{6}=7[/tex]

x=7

Now for the y-axis:

[tex]\displaystyle y=\frac{5y_b+y_a}{6}[/tex]

Substituting:

[tex]\displaystyle y=\frac{5*10+4}{6}=\frac{54}{6}=9[/tex]

y=9

Point P has coordinates (7,9) (last choice)

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