Find the coordinates of the point of division on the line 2x + 3y – 5 =0 which divides the line segment joining the
points (8, –9) and (2, 1).
The distance between the points A (0, 6) and B (0, –2) is
The distance between the points (0, 5) and (–5, 0) is
AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is .
The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the
The points (–4, 0), (4, 0) and (0, 3) are the vertices of a
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is
The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is .
If P \left(\frac{a}{3}, 4\right) is the mid point of the line segment joining the points Q(–6, 5) and R(–2, 3), what is the value of a?
A circle drawn with origin as the centre passes through a point (13/2,0). The point which does not lie in the interior of the circle is
A line intersects the y–axis and x–axis at points P and Q respectively. If (2, –5) is the mid–point of PQ, then co–ordinates of P and Q are respectively.
The area of the triangle with vertices (a, b + c) (b, c + a) and (c, a +b) is
If the distance between the point (4, p) and (1, 0) is 5, then the value of p is
If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then
The perpendicualr bisector of the line segment joining the points A(1, 5) and B(4,6) cuts y–axis at
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then
The distance of the point P (–6, 8) from the origin is .
The distance of the point P (2, 3) from the x-axis is
The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure is
State whether the following statment is true or false.
Points A (3, 1), B (12, –2) and C (0, 2) cannot be the vertices of a triangle.
△ABC with vertices A (–2, 0), B (2, 0) and C (0, 2) is similar to △DEF with vertices D (–4, 0) E (4, 0) and F (0, 4).
Point P (0, 2) is the point of intersection of y–axis and perpendicular bisector of line segment joining the points A (–1, 1) and B (3, 3).
The points (0, 5), (0, –9) and (3, 6) are collinear.
Point P (– 4, 2) lies on the line segment joining the points A (– 4, 6) and B (– 4, – 6).
Points A (4, 3), B (6, 4), C (5, –6) and D (–3, 5) are the vertices of a parallelogram.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5).
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a recangle.
The point A(2,7) lies on the perpendicular bisector of line segment joining the points P(6,5) and Q(0,–4).
Point P(5, –3) is one of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5).
Points A(–6, 10), B(–4, 6) and C(3, –8) are collinear such that AB = 2/9 AC.
Find the points on the x–axis which are at a distance of 2√5 from the point (7, –4). How many such points are there?
Find the value of a, if the distance between the points A (–3, –14) and B (a, –5) is 9 units.
What type of a quadrilateral do the points A (2, –2), B (7, 3), C (11, –1) and D (6, –6) taken in that order, form?
The point P(–2, 4) lies on a cirle of radius 6 and centre (3, 5).
The coordinates of one end point of a diameter AB of a circle are A(4, -1) and the coordinates of the centre are C(1, -3). Find the coordinates of B.
How many points are there which are equidistant from the points A (–5, 4) and B (–1, 6)?
**Find the coordinates of the point Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points A (–5, –2) and B(4, –2) and name the type of triangle formed by the points Q, A and B.**
If point P(9a – 2, –b) divides the line segment joining the points A(3a + 1, –3) and B(8a, 5) in the ratio 3 : 1, then find the values of a and b.
If the point A (2, – 4) is equidistant from P (3, 8) and Q (–10, y), find the values of y.
In what ratio does the x–axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.
If the centre of circle is (2a, a – 7) then find the values of a if the circle passes through
the point (11, –9) and has diameter 10√2 units.
The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio of 1 : 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.
Find the value of k if the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear
Find the coordinates of the point R on the line segment joining the points P(–1, 3) and Q(2, 5) such that PR = 3/5 PQ
If ,D(-1/2, 5/2) E(7, 3) and F(/2 7/2) are the mid–points of sides of ΔABC, find the area of ΔABC
The points A(2, 9), B(a, 5) and C(5, 5) are the verticles of a ΔABC right angled at B. Find the values of a.
Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.
Find the area of the triangle whose vertices are (–8, 4), (–6, 6) and (–3, 9).
The points A(2, 9), B(2, 5) and C(5, 5) are the verticles of a ΔABC right angled at B. Find the area of ΔABC.
If the point A (2, – 4) is equidistant from P (3, 8) and Q (–10, y), find distance PQ.
If (a, b) is mid–point of the line segment joining points A(10, –6) and B(k, 4) and a – 2b = 18, then find the value of k.
If (a, b) is mid–point of the line segment joining points A(10, –6) and B(22 4) and a – 2b = 18, find the distance of AB.
Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, -3). Also find the value of x.
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of △ ADE.
The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC. The median from A meets BC at D. Find the coordinates of the point D.
If the points A(1, –2), B(2, 3), C(a, 2) and D(–4, –3) from a parallelogram, find the value of a.
Student of a school are standing in rows and column in their playground for a drill practice. A, B, C, D are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
Ayush start walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines.) If the house is situated at (2, 4) bank at (5, 8) school at (13, 14) and office at (13, 26) and coordinates are in km.
If the points A(1, –2), B(2, 3), C(a, 2) and D(–4, –3) from a parallelogram, find the height of the parallelgoram taking AB as base.
In the figure ABC is a triangle with vertices A (x1, y1), B (x2, y2) and C (x3 y3) and D is the mid-point of BC. Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
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