The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B are (11 , -13)
Step-by-step explanation:
If point (x , y) divides the line segment whose endpoints are [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] at the ratio [tex](m_{1}:m_{2})[/tex] from point [tex](x_{1},y_{1})[/tex] , then
- [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
- [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
∵ A (3 , -5) and B (13 , -15) are the end points of a line segment
∴ [tex]x_{1}[/tex] = 3 and [tex]x_{2}[/tex] = 13
∴ [tex]y_{1}[/tex] = -5 and [tex]y_{2}[/tex] = -15
∵ (x , y) is located on the line segment at [tex]\frac{4}{5}[/tex] of the
way from A to B
- That means the distance from A to (x , y) is 4 units and the
distance from (x , y) to B is 1 unit [5 - 4 = 1]
∴ [tex](m_{1}:m_{2})[/tex] = 4 : 1
∵ [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{-65}{5}[/tex]
∴ y = -13
The y-coordinate of the point is -13
The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B are (11 , -13)
Learn more:
You can learn more about the midpoint of a segment in brainly.com/question/10772249
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