Advertisements
Advertisements
Question
Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .
Solution
A (16, − 18), B (3, −6), C (−10, 6)
Slope of AB = \[\frac{y_2 - y_1}{x_2 - x_1} = \frac{- 6 + 18}{3 - 16} = - \frac{12}{13}\]
Slope of BC = \[\frac{y_2 - y_1}{x_2 - x_1} = \frac{6 + 6}{- 10 - 3} = - \frac{12}{13}\]
Since, Slope of AB = Slope of BC = \[- \frac{12}{13}\]
Therefore, the given points are collinear.
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 the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
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 value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{2\pi}{3}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
Find the slope of a line passing through the following point:
(3, −5), and (1, 2)
Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).
Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).
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 intersecting the x-axis at a distance of 3 units to the left of origin.
Find the equations of the bisectors of the angles between the coordinate axes.
Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from 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.
If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.
The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
Find the acute angle between the lines 2x − y + 3 = 0 and x + y + 2 = 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.
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
The equation of a line passing through the point (7, - 4) and perpendicular to the line passing through the points (2, 3) and (1 , - 2 ) is ______.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
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.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
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 ______.
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)`
Slope of a line which cuts off intercepts of equal lengths on the axes is ______.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
