Advertisements
Advertisements
Question
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
Advertisements
Solution
The points (3, 4) and (2, – 6) are situated on the opposite of the line 3x – 4y – 8 = 0.
Explanation:
Given line is 3x – 4y – 8 = 0 ......(i)
And the given points are (3, 4) and (2, – 6).
For point (3, 4), line becomes = 3(3) – 4(4) – 8
= 9 – 16 – 8
= 9 – 24
= – 15 < 0
For the point (2, – 6), line becomes = 3(2) – 4(– 6) – 8
= 6 + 24 – 8
= 30 – 8
= 22 > 0
So, the points (3, 4) and (2, – 6) are situated on the opposite sides of 3x – 4y – 8 = 0.
APPEARS IN
RELATED QUESTIONS
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?
Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[- \frac{\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (5, 6) and (2, 3); through (9, −2) and (6, −5)
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)
Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.
Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
Find the equation of a straight line with slope 2 and y-intercept 3 .
Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.
Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.
Find the coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).
Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
Prove that the points (2, −1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is
Point of the curve y2 = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is ______.
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.
If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.
Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
| Column C1 | Column C2 |
| (a) The coordinates of the points P and Q on the line x + 5y = 13 which are at a distance of 2 units from the line 12x – 5y + 26 = 0 are |
(i) (3, 1), (–7, 11) |
| (b) The coordinates of the point on the line x + y = 4, which are at a unit distance from the line 4x + 3y – 10 = 0 are |
(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.
