[4 marks sum]

Question 14 Marks

The line segment joining the points $(3,-4)$, and $(1,2)$ is trisected at the points P and Q . If the coordinates of P and Q are $(p,-2)$ and $\left(\frac{5}{3}, q\right)$ respectively, find the values of $p$ and $q$.

Answer

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Question 24 Marks

The line segment joining $P (-4,5)$ and $Q (3,2)$ intersects the $y$-axis at R . PM and QN are perpendiculars from P and Q on $x$-axis. Find:
(a) the ratio $PR : RQ$
(b) the coordinates of R
(c) the area of the quadrilateral PMNQ.

Answer

Self

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Question 34 Marks

Find the lengths of the medians of a triangle whose vertices are $A (7,-3), B (5,3)$ and $C (3,-1)$.

Answer

Self

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Question 44 Marks

P and Q are the points on the line segment joining the points $A (3,-1)$ and $B (-6,5)$ such that $AP = PQ = QB$. Find the co-ordinates of P and Q .

Answer

Self

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Question 54 Marks

The base BC of an equilateral triangle ABC lies on $y$-axis. The coordinates of point C are $(0,-3)$. If the origin is the mid-point of the base BC , find the coordinates of the points A and B .

Answer

Self

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Question 64 Marks

If the coordinates of the midpoints of the sides of a triangle are $(1,2),(0,-1)$ and $(2,-1)$, find the coordinates of its vertices.

Answer

Self

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Question 74 Marks

Find the ratio in which the point $(-3, p)$ divides the line segment joining the points $(-5,-4)$ and $(-2,3)$. Hence, find the value of $p$.

Answer

Self

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Mathematics [4 marks sum]

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