Advertisements
Advertisements
Question
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).
Advertisements
Solution
Mid point of the line segment joining the points P(0, –4) and B(8, 0)
`"x" = ("x"_1 + "x"_2)/2`
= `(0 + 8)/2`
= 4
y = `("y"_1 + "y"_2)/2`
= `(-4 + 0)/2`
= `(-4)/2`
= −2
= The midpoint of PB has coordinates (4, −2) of M.
The coordinates of the origin point 0 are (0, 0).
∴ OM = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
= `(-2 -0)/(4 - 0)`
= `(-2)/4`
= `(-1)/2`
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.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines.
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 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:
\[\frac{3\pi}{4}\]
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?
What can be said regarding a line if its slope is zero ?
Consider the following 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 value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.
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 y-intercept 3 .
Find the equations of the bisectors of the angles between the coordinate axes.
Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).
Find the angles between the following pair of straight lines:
x − 4y = 3 and 6x − y = 11
Prove that the straight lines (a + b) x + (a − b ) y = 2ab, (a − b) x + (a + b) y = 2ab and x + y = 0 form an isosceles triangle whose vertical angle is 2 tan−1 \[\left( \frac{a}{b} \right)\].
Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 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 ______.
If x + y = k is normal to y2 = 12x, then k is ______.
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.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.
The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and
| Column C1 | Column C2 |
| (a) Through the point (2, 1) is | (i) 2x – y = 4 |
| (b) Perpendicular to the line (ii) x + y – 5 = 0 x + 2y + 1 = 0 is |
(ii) x + y – 5 = 0 |
| (c) Parallel to the line (iii) x – y –1 = 0 3x – 4y + 5 = 0 is |
(iii) x – y –1 = 0 |
| (d) Equally inclined to the axes is | (iv) 3x – 4y – 1 = 0 |
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). The co-ordinates of the point A is ______.
The three straight lines ax + by = c, bx + cy = a and cx + ay = b are collinear, if ______.
