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12 cards from this deck
Finds coordinates of point dividing line in given ratio
(qx1+px2p+q,qy1+py2p+q)\left(\frac{qx_1+px_2}{p+q}, \frac{qy_1+py_2}{p+q}\right)(p+qqx1+px2,p+qqy1+py2)
Point between two given points on line segment
Both horizontal and vertical
Weighted averages
qx1+px2p+q\frac{qx_1 + px_2}{p + q}p+qqx1+px2
qy1+py2p+q\frac{qy_1 + py_2}{p + q}p+qqy1+py2
Distance A to C vs C to B in ratio p:qp:qp:q
AC:CBAC:CBAC:CB differs from AC:ABAC:ABAC:AB
First point's coordinate × second ratio number (e.g., x1x_1x1 × qqq)
Check geometric sense with ratio
Ratios act as weights for endpoint coordinates
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