Advertisements
Advertisements
Question
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
Advertisements
Solution
- We are given that co-ordinates of P is (x1, y1) and Q is (x2 Y2)·
Distance between the points P(x1, y1) and Q (x2 y2) is
PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)` ...(1)
When PQ is parallel to y-axis then x1 = x2 from (1), we have
PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((x_1 - x_1)^2 + (y_2 - y_1)^2) = |y_2 - y_1|` - When PQ is parallel to x-axis, then y1 = y2 from (1), we have
PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((x_2 - x_1)^2 +0) = |x_2 - x_1|`
APPEARS IN
RELATED QUESTIONS
The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
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 values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is
- Parallel to the x-axis,
- Parallel to the y-axis,
- Passing through the origin.
Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
Find the slope of a line passing through the following point:
(3, −5), and (1, 2)
What can be said regarding a line if its slope is positive ?
What can be said regarding a line if its slope is negative?
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
Without using the distance formula, show that points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).
Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
Find the equation of a straight line with slope −2 and intersecting the x-axis at a distance of 3 units to the left of origin.
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 angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
Find the angles between the following pair of straight lines:
x − 4y = 3 and 6x − y = 11
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 is
The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
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.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
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.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are y – 3 = `(2 +- sqrt(3)) (x - 2)`.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
