Advertisements
Advertisements
Question
Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.
Advertisements
Solution
Given, points P(k, −1), Q(2, 1) and R(4, 5) are collinear.
∴ Slope of PQ = Slope of QR
∴ `(1 - (-1))/(2 - "k") = (5 - 1)/(4 - 2)`
∴ `2/(2 - "k") = 4/2`
∴ 4 = 4 (2 − k)
∴ 1 = 2 − k
∴ k = 2 − 1 = 1
APPEARS IN
RELATED QUESTIONS
Find the slope of the following line which passes through the points:
A(2, −1), B(4, 3)
Find the slope of the following line which passes through the points:
C(−2, 3), D(5, 7)
If the X and Y-intercepts of lines L are 2 and 3 respectively then find the slope of line L.
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 acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).
If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1
Select the correct option from the given alternatives:
The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is
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:
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)
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) and (– 2, 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
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
Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line
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 |
What is the actual length of the spring
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
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 slopes of the escalator at the turning points
Choose the correct alternative:
Straight line joining the points (2, 3) and (−1, 4) passes through the point (α, β) if
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
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 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 ______.
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?
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.
The equation of the line passing through the point (–3, 1) and bisecting the angle between co-ordinate axes is ______.
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.
