Pre-Calc Question

[Craft35]

The midpoint formula could be considered to be the “halfway” formula since it gives us the point that is ½ of the distance from the point P(x sub 1, y sub 1) to the point Q(x sub 2, y sub 2). Develop an “m-nth way” formula that gives the point R(X sub 3, y sub 3) that is m/n of the distance from P to Q (assume m and n are positive integers with m < n).

would either of these be correct?

X = P + (m/n) * (Q - P)

Or

( m(x1+x2)/n, m(y1+y2)/n )

 

[Deleted member 4993]

The midpoint formula could be considered to be the “halfway” formula since it gives us the point that is ½ of the distance from the point P(x sub 1, y sub 1) to the point Q(x sub 2, y sub 2). Develop an “m-nth way” formula that gives the point R(X sub 3, y sub 3) that is m/n of the distance from P to Q (assume m and n are positive integers with m < n).

would either of these be correct?

X = P + (m/n) * (Q - P)

Or

( m(x1+x2)/n, m(y1+y2)/n )

Draw a sketch of the sitution.

Create similar triangles and use proportions.