Advertisements
Advertisements
प्रश्न
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).
उत्तर
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
संबंधित प्रश्न
Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
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.
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.
Line through the points (−2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
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 straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
Find the angles between the following pair of straight lines:
3x − y + 5 = 0 and x − 3y + 1 = 0
Find the angles between the following pair of straight lines:
x − 4y = 3 and 6x − y = 11
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 acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.
The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.
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.
If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
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 ______.
