Q1.
Find the acute angle between the lines
and
.
Q2.
Using the formula for finding the area of triangle, prove that the points
are collinear.
Q3.
Find the values of
parallel to the
Q4.
In what ratio is the line joining
Q5.
Show that the line joining the points
joining the points
.
is perpendicular to the line
Q6.
Find the area of the triangle formed by the lines
.
,
Q7.
Find the equation of the line passing through the point
line joining the points
.
Q8.
If
sides.
Q9.
Find the equations of the lines which cut off intercepts on the axis whose sum and
product are
respectively.
Q10.
Show that the lines
the point of intersection.
are concurrent. Find also
Q11.
If
The median through
, find the equation of (i)
Q12.
Find the equation of a line whose perpendicular distance from the origin is units
and the angle between the positive direction of
and the perpendicular is
for which the line
, and (ii) passes through the origin.
(i) is
divided by the line
are the vertices of the
are the vertices of a
(ii) The altitude through
?
and
and parallel to the
. Find the equation of its
Q13.
Reduce the equation
to the intercept form, and hence find the
length of the portion of the line intercepted between the axis.
Q14.
Find the equation of the line passing through the intersection of the lines
and
, and parallel to the line
.
Q15.
Find the values of
line
for which the length of perpendicular from the point
is units.
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.
on the
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Q16.
Find the equation of a line which passes through the point
intercept on the
exceeds the intercept on the
and whose
by .
Q17.
Find the equation of the perpendicular bisector of the line joining the points
.
Q18.
A line passes through the points
makes an obtuse angle with
Q19.
Q20.
Reduce the equation
hence find the values of
. Show that the line
.
to the normal form
, and
.
Find the equation of a line drawn perpendicular to the line
point, where it meets the
through the
.
Answers
A1.
A2.
Hint: Show that the area of
A3.
(i)
.
(ii)
A4.
A5.
Hint: Find the slopes
of the lines
, and show that
.
A6.
A7.
A8.
A9.
A10.
Point of intersection is
A11.
(i)
.
(ii)
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A12.
A13.
A14.
A15.
A16.
A17.
A18.
Hint: Show that the slope of the line
is negative.
A19.
A20.
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