Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(10, 8), B(18, 12); 1 to 3

The coordinates of P are (12,9)

Step-by-step explanation:

Equations

We are given the endpoints of the segment AB: A(10,8) B(18,12).

It's required to find the coordinates of point P(x,y) along the segment AB such that:

The ratio of the distances is the same as the ratio of their respective coordinates:

Since

Then:

Multiplying by 3 (18-x):

3( x - 10 )= 18 - x

3x - 30 = 18 - x

Adding x and 30:

4x = 48

x = 12

Similarly:

Multiplying by 3 (12-y):

3( y - 8 ) = 12 - y

3y - 24 = 12 - y

Adding y and 24:

4y = 36

y = 9

The coordinates of P are (12,9)

step-by-step explanation:

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2