The point located on the line segment between A and B is (11 , -11)
Step-by-step explanation:
If point (x , y) divides a segment whose endpoints are [tex](x_{1},y_{1})[/tex] , [tex](x_{2},y_{2})[/tex] , at a ratio [tex]m_{1}:m_{2}[/tex] from the first point, then
∵ Point (x , y) located on the line segment AB between A and B
∵ A = (3 , 5) and B = (13 , -15)
∴ [tex]x_{1}[/tex] = 3 and [tex]x_{2}[/tex] = 13
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = -15
∵ Point (x , y) is [tex]\frac{4}{5}[/tex] of the way from A to B
- That means the line from A to be is 5 parts where the distance
from point A to point (x , y) is 4 parts and the distance from point
(x , y) to point B is 1 part (5 - 4 = 1)
∴ [tex]m_{1}:m_{2}[/tex] = 4 : 1
By using the two rules above
∵ [tex]x=\frac{(3)(1)+(13)(4)}{4+1}[/tex]
∴ [tex]x=\frac{3+52}{5}[/tex]
∴ [tex]x=\frac{55}{5}[/tex]
∴ x = 11
∴ The x-coordinate of the point is 11
∵ [tex]y=\frac{(5)(1)+(-15)(4)}{4+1}[/tex]
∴ [tex]y=\frac{5+(-60)}{5}[/tex]
∴ [tex]y=\frac{-55}{5}[/tex]
∴ y = -11
∴ The y-coordinate of the point is -11
The point located on the line segment between A and B is (11 , -11)
Learn more:
You can learn more about the division point of a line segment in brainly.com/question/10364988
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