[4 marks sum]

Question 14 Marks

A and B are two points on the $x$-axis and $y$-axis respectively. $P (2,-3)$ is the mid point of AB . Find the
(a) coordinates of A and B .
(b) slope of line AB .
(c) equation of line $A B$.

Answer

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Question 24 Marks

Points A and B have coordinates $(7,-3)$ and $(1,9)$ respectively. Find:
(a) the slope of AB .
(b) the equation of the perpendicular bisector of the line segment AB .
(c) the value of $p$ if $(-2, p)$ lies on it.

Answer

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Question 34 Marks

Find the value of $p$ if the lines, $5 x-3 y+2=0$ and $6 x-p y+7=0$ are perpendicular to each other. Hence find the equation of a line passing through $(-2,-1)$ and parallel to $6 x-p y+7=0$.

Answer

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Question 44 Marks

A line AB meets $x$-axis at A and $y$-axis at $B . P (4,-1)$ divides AB in the ratio 1 : 2.
(a) Find the coordinates of A and B.
(b) Find the equation of the line through P and perpendicular to AB .

Answer

Self

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Question 54 Marks

Find the equation of the perpendicular from the point $(1,-2)$ on the line $4 x-3 y-5=0$. Also, find the co-ordinates of the foot of the perpendicular.

Answer

Self

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Question 64 Marks

If the coordinates of the vertex A of a square ABCD are $(3,-2)$ and the equation of diagonal BD is $3 x-7 y+6=0$, find the equation of the diagonal AC . Also, find the co-ordinates of the centre of the square.

Answer

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Question 74 Marks

A straight line makes positive intercepts on the co-ordinates axes whose sum is 7 . If the line passes through the point $(-3,8)$, find its equation.

Answer

Self

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Question 84 Marks

A straight line passes through $P (2,1)$ and cuts the $x$ and $y$-axis at points $A , B$ respectively. If $BP : PA =3: 1$, find :
(a) the coordinates of A and B
(b) the equation of the line AB

Answer

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Question 94 Marks

Find the equation of the line perpendicular to the line joining the points $A (1,2)$ and $B (6,7)$ and passing through the point which divides the line segment AB in the ratio $3: 2$.

Answer

Self

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Mathematics [4 marks sum]

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