91Ó°ÊÓ

Find the projection of \(A B\) on the coordinate axes where the coordinates of the points \(\mathrm{A}\) and \(\mathrm{B}\) are \((4,4)\) and \((9,10)\), respectively.

Find the coordinates of the point \(\mathrm{P}(\mathrm{x}, \mathrm{y})\) which divides the following segments into the given ratios: (1) \(\mathrm{P}_{1}(4,4) . \mathrm{P}_{2}(8,8), \mathrm{r}_{1}: \mathrm{I}_{2}=-1: 2\) (2) \(\mathrm{P}_{1}(4,9), \mathrm{P}_{2}(9,10), \mathrm{r}_{1}: \mathrm{r}_{2}=0\) : a where a is a real constant.

Find the midpoint of the segment from \(\mathrm{R}(-3,5)\) to \(\mathrm{S}(2,-8)\).

What are the coordinates of the midpoint of a line segment joining \(\mathrm{P}(-2,1)\) and \(\mathrm{Q}(6,4) ?\)

Determine the coordinates of the midpoint of the line segment joining the points \((3,-8)\) and \((-7,5)\).

A line segment \(A B\) is \(7(1 / 2)\) in. long. Locate the point \(C\) between \(\mathrm{A}\) and \(\mathrm{B}\) so that \(\mathrm{AC}\) is \(3 / 2 \mathrm{in}\). shorter than twice \(\mathrm{CB}\).

Find the point \(Q\) that is \(3 / 4\) of the way from the point \(\mathrm{P}(-4,-1)\) to the point \(\mathrm{R}(12,11)\) along the segment PR.

What is the distance between the points \((2,3)\) and \((7,11) ?\)

Find the distance from the origin to the point \((\mathrm{x}, \mathrm{y})\).

Find the distance between the given pair of points, and find the slope of the line segment joining them. \((3,-5),(2,4)\)