Question

The points A, B, C, D, E, F, G, H, I, J AND K lie on the number line as shown below. If AB=BC, DE=EF, GH=HI=IJ=JK, which rational numbers do the points B, E, H and J represent?

Answer 1

Answer:

$AB = BC \\ means \: B \: is \: midpoint \: of \: AC$

$so \: point \: B = \frac{ - 3 + ( - 2)}{2} = \frac{ - 5}{2} = - 2.5$

$DE = EF\\ means \: E\: is \: midpoint \: of \: DF$

$so \: point \: E= \frac{ - 1 + 0}{2} = \frac{ - 1}{2} = - 0.5$

$GH = HI = IJ= JK \\ means \: H \: is \: midpoint \: of \: GI \: and \: where \\ J \: is \: midpoint \: of \: IK$

$point \: H = \frac{1 + 2}{2} = \frac{3}{2} = 1.5$

$point \: J= \frac{2 + 3}{2} = \frac{5}{2} = 2.5$