Question

Lisa is partitioning line segment a b so that a point C divides a line segment into the ratio 2 to 3 Nikki said that she can do the same thing but by multiplying point a by the fraction of 2/5 since this is the part to the whole ratio equivalent do you agree or disagree with Nikki justify your answer

Answer 1

This is true because:

the ratio 2 to 3 = 2:3

Is equivalent to :

2/(3+2) = 2/5

If you want to express a ratio a:b as a fraction, you can always use this formula:

a:b = a/(a+b)

You can use the following formula:

If d(xp,yp) divides a line segment form A(x1,y1) to B(x2,y2) in the ratio a:b, then:

xp = x1 + a/(a+b) * (x2 - x1)

yp = y1 + a/(a+b) * (y2 - y1)

So:

xp = 1 + 2/5*(16-1) = 7

yp = 4 + 2/5*(14 - 4) = 8