Plane and solid analytic geometry, by William F. Osgood and William C. Graustein.

26

ANALYTIC GEOMETRY

Suggestion. Determine the ratio in which the point divides
the line-segment between the two given points.
15. Prove that the sum of the squares of the distances of
any point in the plane of a given rectangle to two opposite
vertices equals the sum of the squares of the distances from it
to the two other vertices.
Suggestion. Choose the axes of coordinates skillfully.
16. If D is the mid-point of the side BC of a triangle ABC,
prove that
AB2+ AC2=2 AD2 + 2 BD2.
17. Show that the lines joining the mid-points of opposite
sides of a quadrilateral bisect each other.
18. Prove that the lines joining the mid-points of adjacent
sides of a quadrilateral form a parallelogram.
19. Prove that, if the diagonals of a parallelogram are equal,
the parallelogram is a rectangle.
20. If two medians of a triangle are equal, show that the
triangle is isosceles.