Geometric reasoning

Question 1

Section formula on a the number line

Answer 1

(nx1+mx2)/(m+n)

Question 2

Section formula on the coordinate plane

Answer 2

(nx1+mx2)/(m+n), (ny1+my2)/(m+n)

Question 3

Midpoint formula on the number line

Answer 3

(x1+x2)/2

Question 4

Midpoint formula the coordinate plane

Answer 4

(x1+x2)/2,(y1+y2)/2

Question 5

Weighted average on the number line

Answer 5

(w1x1+w2x2)/(w1+w2)

Question 6

Weighted average on the coordinate plane

Answer 6

(w1x1+w2x2)/(w1+w2),(w1y1+w2y2)/(w1+w2)