Question 33

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Jambmaths question: 

The distance between the point (4,3) and the intersection of y = 2x + 4 and y = 7 – x

Option A: 

$\sqrt{13}$

Option B: 

$3\sqrt{2}$

Option C: 

$\sqrt{26}$

Option D: 

$10\sqrt{5}$

Jamb Maths Solution: 

First, we need to obtain the point of intersection of the two lines y = 2x + 4 and y = 7 – xTo get the point of intersection, we solve the two equations simultaneously$y=2x+4----(i),\text{ }y=7-x----(ii)$Substitute y =7 – x into (i)$7-x=2x+4,\text{  }3x=3,\text{ }x=1$Substitute 1 for x in y = 7 – xy = 6(x, y) = (1, 6)The diagram is rough sketchThe distance between (1, 6) and (4,3) is$d=\sqrt{{{(1-4)}^{2}}+{{(6-3)}^{2}}}=\sqrt{{{3}^{2}}+{{3}^{2}}}=\sqrt{18}=3\sqrt{2}$

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