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

Question

Infinity Learn · Accepted Answer

Let the point R (x$$,y, $$z) divides PQ in the ratio k:$$1$$.⇒k×$$8+1$$×$$2k+1=4$$⇒$$8k+2k+1=4$$⇒$$8k+2=4k+4$$⇒$$8k$$−$$4k=4$$−$$2$$⇒$$4k=2$$⇒$$k=12$$⇒k:$$1=1$$:$$2Hence$$, the point R divides PQ internally in the ratio $$1$$ : $$2$$.Therefore, $$y-coordinate$$ of $$R=1$$×$$0+2$$×$$($$−$$3)1+2=$$−$$63=$$−$$2and$$ $$z-coordinate$$ of $$R=1$$×$$10+2$$×$$41+2=10+83=183=6Hence$$, coordinate of 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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