Advertisements
Advertisements
Question
Answer the following question:
Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)
Solution
Since P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3), the points P, A, B are collinear.
∴ slope of AP = slope of AB
∴ `("k" - 2)/(1 - 2) = (3 - 2)/(3 - 2)`
∴ `("k" - 2)/(-1) = 1/1` = 1
∴ k – 2 = –1
∴ k = 1
APPEARS IN
RELATED QUESTIONS
Find the slope of the following line which passes through the points:
C(−2, 3), D(5, 7)
Find the slope of the line whose inclination is 30°
Find the slope of the line whose inclination is `pi/4`
Without using Pythagoras theorem show that points A(4, 4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.
Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise
Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.
Find the acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).
A line passes through points A(x1, y1) and B(h, k). If the slope of the line is m then show that k − y1 = m(h − x1)
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
Select the correct option from the given alternatives:
If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k
Answer the following question:
Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9
Answer the following question:
Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h
Find the equation of the lines passing through the point (1,1) with slope 3
Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis
If p is length of perpendicular from origin to the line whose intercepts on the axes are a and b, then show that `1/("p"^3) = 1/("a"^2) + 1/("b"^2)`
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
An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance between the place and the target
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using any other method
A 150 m long train is moving with constant velocity of 12.5 m/s. Find the equation of the motion of the train
A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross a pole
A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross the bridge of length 850 m
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 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 |
What is the actual length of the spring
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 |
If the spring has to stretch to 9 cm long, how much weight should be added?
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
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 heights at which the escalator changes its direction
Choose the correct alternative:
The y-intercept of the straight line passing through (1, 3) and perpendicular to 2x − 3y + 1 = 0 is
If one of the lines given by kx2 + 2xy – 3y2 = 0 is perpendicular to the line 3x + 5y+ 1 = 0, then the value of k is ______.
The locus of the point of intersection of the lines xcosα + ysinα = α and xsinα – ycosα = b(where α is a variable) is ______.
The number of possible tangents which can be drawn to the curve 4x2 – 9y2 = 36, which are perpendicular to the straight line 5x + 2y – 10 = 0 is ______.
The coordinates of vertices of base BC of an isosceles triangle ABC are given by B(1, 3) and C(–2, 7) which of the following points can be the possible coordinates of the vertex A?
The locus of the midpoint of the portion intercept between the axes by the line xcosa + ysina = P where P is a constant is ______.
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 = ______.
