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Question Number 32838 by Rio Mike last updated on 03/Apr/18

$$thepointsM(1,1),N(2,4)andR(3,q)$$$$lieontheresamestraightline.$$$$findthecoordinatesofR$$

Commented by Rasheed.Sindhi last updated on 03/Apr/18

$$M(2,4)=N(2,4)\mathrm{is}\mathrm{one}\mathrm{point}.\mathrm{So}\mathrm{there}\mathrm{are}$$$$\mathrm{only}\mathrm{two}\mathrm{points}!$$

Commented by Rio Mike last updated on 03/Apr/18

$$pleaseredoquestionwaswrong$$

Answered by MJS last updated on 03/Apr/18

$$y=kx+d$$$$\mathrm{for}M:1=1k+d\Rightarrow d=1-k\left(\mathrm{I}\right)$$$$\mathrm{for}N:4=2k+d\left(\mathrm{II}\right)$$$$\mathrm{I}\mathrm{in}\mathrm{II}:4=2k+1-k\Rightarrow k=3\Rightarrow d=-2$$$$y=3x-2$$$$\mathrm{for}\mathrm{R}:y=3\times 3-2=7$$

Answered by Rasheed.Sindhi last updated on 04/Apr/18

$$\mathrm{AnOther}\mathrm{method}$$$$\mathrm{Slope}\mathrm{of}\overline{\mathrm{MN}}=\mathrm{Slope}\mathrm{of}\overline{\mathrm{NR}}[\because \overline{\mathrm{MN}}\mathrm{or}\overline{\mathrm{NR}}\mathrm{is}\mathrm{same}\mathrm{line}]$$$$\frac{4-1}{2-1}=\frac{\mathrm{q}-4}{3-2}$$$$\mathrm{q}-4=3$$$$\mathrm{q}=7$$

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