Find the coordinats of P

Mathematics

1 answer:

Crazy boy [7]2 years ago

5 0

$\textit{internal division of a line segment using ratios} \\\\\\ A(8,6)\qquad B(-2,-9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(8,6)=3(-2,-9)$

$(\stackrel{x}{16}~~,~~ \stackrel{y}{12})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{-27})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{16-6}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{12-27}}{3+2} \right)} \\\\\\ P=\left( \cfrac{10}{5}~~,~~\cfrac{-15}{5} \right)\implies P=(2~~,~~-3)$

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Alexxx [7]

$\measuredangle BAC = 29°$

Answer:

$\measuredangle BOC =58°$

Step-by-step explanation:

$\measuredangle BDC = 29°...(Given) \\\because \measuredangle BAC = \measuredangle BDC\\(\angle 's \: subtended \: by\: same\: arc) \\\huge \purple {\boxed {\therefore \measuredangle BAC = 29°}} \\\\$

Since, angle subtended on the center of the circle is twice the angle subtended on the circumference of the circle.

$\therefore \measuredangle BOC =2\times \measuredangle BDC\\\therefore \measuredangle BOC =2\times 29°\\\huge \red {\boxed {\therefore \measuredangle BOC =58°}} \\$