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9. Geometry and Algebra
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Q1 of 23 Page 220

The coordinates of two points A, B are (3, 2) and (8, 7).

i) Calculate the coordinates of the point P on AB such that AP : PB = 2 : 3


ii) Calculate the coordinates of the point Q on AB such that AQ : QB = 3 : 2

(i) The points are A(3,2) , B(8,7)


AP : PB = 2 : 3(Given)



P(x,y) = (5,4)


(ii) The points are A(3,2) , B(8,7)


AQ : QB = 3 : 2(Given)



Q(x,y) = (6,5)


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3

A parallelogram is drawn with the lines joining (x1, y1) and (x2, y2) to the origin as adjacent sides. What are the coordinates of the fourth vertex?

4

Prove that in any parallelogram, the sum of the square of all sides is equal to the sum of the squares of the diagonals.

2

The coordinates of the vertices of a quadrilateral are (2, 1), (5, 3), (8, 7), (4, 9) in order.

i) Find the coordinates of the midpoints of all sides.


ii) Prove that the quadrilateral with these midpoints as vertices is a parallelogram.

3

In the picture, the midpoints of the sides of the large quadrilateral are joined to draw the small quadrilateral inside.


i) Find the coordinates of the fourth vertex of the small quadrilateral.


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Questions · 23
9. Geometry and Algebra
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