Segment AB has coordinates A(-4, 7) and B(5, 1). Find AP/AB and the coordinates of P that partitions AB such that AP:PB = 1:2. AP/AB= [Select] Coordinates of P: ( [Select] [Select] Hint: (x₁+ m/n (x2-x1). Y₁+ m/n (y2-V₁))

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29-05-2022
Mathematics

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Segment AB has coordinates A(-4, 7) and B(5, 1). Find AP/AB and the coordinates of P that partitions AB such that AP:PB = 1:2. AP/AB= [Select] Coordinates of P: ( [Select] [Select] Hint: (x₁+ m/n (x2-x1). Y₁+ m/n (y2-V₁))

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jdoe0001 jdoe0001 · Answer 1 · 2022-05-29T22:38:33+02:00

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-4,7)\qquad B(5,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-4,7)=1(5,1)[/tex]

[tex](\stackrel{x}{-8}~~,~~ \stackrel{y}{14})=(\stackrel{x}{5}~~,~~ \stackrel{y}{1})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-8 +5}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{14 +1}}{1+2} \right)} \\\\\\ P=\left(\cfrac{-3}{3}~~,~~\cfrac{15}{3} \right)\implies P=(-1~~,~~5)[/tex]

now, the segment AB cut by P in a 1:2 ratio, makes 3 thirds, so the ratio AP/AB is

[tex]\cfrac{AP}{AB}\implies \cfrac{1}{1+2}\implies \cfrac{1}{3}[/tex]

Segment AB has coordinates A(-4, 7) and B(5, 1). Find AP/AB and the coordinates of P that partitions AB such that AP:PB = 1:2. AP/AB= [Select] Coordinates of P: ( [Select] [Select] Hint: (x₁+ m/n (x2-x1). Y₁+ m/n (y2-V₁))​

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Otras preguntas

Segment AB has coordinates A(-4, 7) and B(5, 1). Find AP/AB and the coordinates of P that partitions AB such that AP:PB = 1:2. AP/AB= [Select] Coordinates of P: ( [Select] [Select] Hint: (x₁+ m/n (x2-x1). Y₁+ m/n (y2-V₁))