What is the midpoint of the segment connecting [math]\left(1,2\right)[/math] and [math]\left(5,2\right)[/math]?[br]

What is the midpoint of the segment connecting [math]\left(5,2\right)[/math] and [math]\left(5,10\right)[/math]?[br]

What is the midpoint of the segment connecting [math]\left(1,2\right)[/math] and [math]\left(5,10\right)[/math]?[br]

Find the point that partitions segment [math]AB[/math] in a [math]2:1[/math] ratio.

Calculate [math]C=\frac{1}{3}A+\frac{2}{3}B[/math].[br]

What do you notice about your answers to the first 2 questions?[br]

For 2 new points [math]K[/math] and [math]L[/math], write an expression for the point that partitions segment [math]KL[/math] in a [math]3:1[/math] ratio.

[size=150]Consider the general quadrilateral [math]QRST[/math] with [math]Q=\left(0,0\right)[/math], [math]R=\left(a,b\right)[/math], [math]S=\left(c,d\right)[/math], and [math]T=\left(e,f\right)[/math].[/size][br][br]Find the midpoints of each side of this quadrilateral.[br]

[list][*]Find the point that partitions segment [math]AB[/math] in a [math]1:4[/math] ratio. Label it [math]B'[/math].[br][/*][*]Find the point that partitions segment [math]AD[/math] in a [math]1:4[/math] ratio. Label it [math]D'[/math].[br][/*][*]Find the point that partitions segment [math]AC[/math] in a [math]1:4[/math] ratio. Label it [math]C'[/math].[br][/*][/list][br]Is [math]AB'C'D'[/math] a dilation of [math]ABCD[/math]? Justify your answer.[br]