A point R with x-coordinate 4 lies on the lin | vedclass

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(A) The coordinates of points $P$ and $Q$ are given as $P(2, -3, 4)$ and $Q(8, 0, 10)$.Let $R$ divide the line segment $PQ$ in the ratio $k:1$.By the

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$(4, -2, 6)$

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(A) The coordinates of points $P$ and $Q$ are given as $P(2, -3, 4)$ and $Q(8, 0, 10)$.Let $R$ divide the line segment $PQ$ in the ratio $k:1$.By the section formula,the coordinates of point $R$ are given by $\left(\frac{8k+2}{k+1}, \frac{-3}{k+1}, \frac{10k+4}{k+1}ight)$.It is given that the $x$-coordinate of point $R$ is $4$.$	herefore \frac{8k+2}{k+1} = 4$$\Rightarrow 8k + 2 = 4k + 4$$\Rightarrow 4k = 2$$\Rightarrow k = \frac{1}{2}$.Substituting $k = \frac{1}{2}$ into the coordinates of $R$:$y$-coordinate: $\frac{-3}{\frac{1}{2} + 1} = \frac{-3}{\frac{3}{2}} = -2$.$z$-coordinate: $\frac{10(\frac{1}{2}) + 4}{\frac{1}{2} + 1} = \frac{5 + 4}{\frac{3}{2}} = \frac{9}{\frac{3}{2}} = 6$.Thus,the coordinates of point $R$ are $(4, -2, 6)$.

$A$ point $R$ with $x$-coordinate $4$ lies on the line segment joining the points $P(2, -3, 4)$ and $Q(8, 0, 10)$. Find the coordinates of the point $R$.

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