Advertisements
Advertisements
Question
If P(r, c) is midpoint of a line segment between the axes then show that `x/"r" + y/"c"` = 2
Advertisements
Solution
Let AB be the line segment intercepted between the axes.
Let A be (a, 0) and B be (0, b)
Given P(r, c) is the midpoint of AB
∴ (r, c) = `((0 + "a")/2, ("b" +0)/2)`
r = `"a"/2`, c = `"b"/2`
a = 2r, b = 2c
The equation of the line AB having x-intercept a and y-intercept b is `x/"a" + y/"b"` = 1
Substituting for a, b in the above equation, we have
`x/(2"r") + y/(2"c")` = 1
`x/"r" + y/"c"` = 2
APPEARS IN
RELATED QUESTIONS
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
Select the correct option from the given alternatives:
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y−interecpt is
Answer the following question:
Find the value of k the points A(1, 3), B(4, 1), C(3, k) are collinear
Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3:10
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of F for 38°C
Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12
A straight line is passing through the point A(1, 2) with slope `5/12`. Find points on the line which are 13 units away from A
A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross a pole
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
Draw a graph showing the results.
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Find the equation relating the quantity of gas in the cylinder to the days
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Draw the graph for first 96days
In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the minimum total length of the escalator
Choose the correct alternative:
The line (p + 2q)x + (p − 3q)y = p − q for different values of p and q passes through the point
Choose the correct alternative:
The y-intercept of the straight line passing through (1, 3) and perpendicular to 2x − 3y + 1 = 0 is
The distance of the origin from the centroid of the triangle whose two sides have the equations. x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is `(7/3. 7/3)` is ______.
A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate, axes will lie only in ______.
Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) internally in the ratio 2 : 3.
If planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line then a2 + b2 + c2 = ______.
Find the transformed equation of the straight line 2x – 3y + 5 = 0, when the origin is shifted to the point (3, –1) after translation of axes.
