Find the coordinates of the point which is three-fourth of the way from A (3, 1) to B ( – 2, 5).
P divides the distance between A ( – 2, 1) and B (1, 4) in the ratio of 2 : 1. Calculate the co-ordinates of the point P.
Find the co-ordinates of the points of trisection of the line segment joining the point (3, – 3) and (6, 9).
The line segment joining the points (3, – 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, – 2) and (5/3, q) respectively, find the values of p and q.
Find the co-ordinates of the mid-point of the line segments joining the following pairs of points:
(2, – 3), ( – 6, 7)
(5, – 11), (4, 3)
(a + 3, 5b), (2a – 1, 3b + 4)
A point P divides the line segment joining the points A (3, – 5) and B ( – 4, 8) such that AP/PB = k/1 If P lies on the line x + y = 0, then find the value of k.
The line segment joining the points A (3, 2) and B (5, 1) is divided at the point P in the ratio 1 : 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.
Point P (3, – 5) is reflected to P’ in the x- axis. Also P on reflection in the y-axis is mapped as P”.
Find the co-ordinates of P’ and P”.
Compute the distance P’ P”.
Find the middle point of the line segment P’ P”.
On which co-ordinate axis does the middle point of the line segment P P” lie ?
Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4).
Write down the co-ordinates of A1, the reflection of A in the y-axis.
Write down the co-ordinates of B1, the reflection of B in the x-axis.
Assign the special name to the quadrilateral ABA1B1.
The mid-point of the line segment AB shown in the adjoining diagram is (4, – 3). Write down the co-ordinates of A and B.
Assign the special name to quadrilateral ABC1B1.
The line segment joining A ( – 3, 1) and B (5, – 4) is a diameter of a circle whose centre is C.
find the co-ordinates of the point C.
The mid-point of the line segment joining the points (3m, 6) and ( – 4, 3n) is (1, 2m – 1).
Find the values of m and n.
The co-ordinates of the mid-point of the line segment PQ are (1, – 2). The co-ordinates of P are ( – 3, 2).
Find the co-ordinates of Q.
AB is a diameter of a circle with centre C ( – 2, 5). If point A is (3, – 7).
Find: the length of radius AC.
Find: the coordinates of B.
Find the reflection (image) of the point (5, – 3) in the point ( – 1, 3).
The line segment joining A(-1,5/3) the points B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects y-axis.
Calculate the value of a.
Calculate the length of the median through the vertex A of the triangle ABC with vertices A (7, – 3), B (5, 3) and C (3, – 1).
The vertices of a triangle are A ( – 5, 3), B (p, – 1) and C (6, q). Find the values of p and q if the centroid of the triangle ABC is the point (1, – 1).
Calculate the co-ordinates of P.
The point P ( – 4, 1) divides the line segment joining the points A (2, – 2) and B in the ratio of 3 : 5.
Find the point B.
In what ratio does the point (5, 4) divide the line segment joining the points (2, 1) and (7 ,6) ?
The line segment joining A (2, 3) and B (6, – 5) is intercepted by the x-axis at the point K. Write the ordinate of the point k. Hence, find the ratio in which K divides AB. Also, find the coordinates of the point K.
If A ( – 4, 3) and B (8, – 6), find the length of AB.
Calculate the ratio in which the line segment joining (3, 4) and( – 2, 1) is divided by the y-axis.
In what ratio does the line x – y – 2 = 0 divide the line segment joining the points (3, – 1) and (8, 9)? Also, find the coordinates of the point of division.
Given a line segment AB joining the points A ( – 4, 6) and B (8, – 3).
Find: the ratio in which AB is divided by the y-axis.
Find: the coordinates of the point of intersection.
Write down the co-ordinates of the point P that divides the line joining A ( – 4, 1) and B (17,10) in the ratio 1 : 2.
Find: the length of AB.
In what ratio does the y-axis divide the line AB ?
Calculate the distance OP where O is the origin.
A (2, 5), B ( – 1, 2) and C (5, 8) are the vertices of a triangle ABC. P and Q are points on AB and AC respectively such that AP : PB = AQ : QC = 1 : 2.
Find the co-ordinates of P and Q.
If C is the midpoint is AB. Write down the co-ordinates of the point C1, the reflection of C in the origin.
Find the third vertex of a triangle if its two vertices are ( – 1, 4) and (5, 2) and midpoint of one sides is (0, 3).
If the points A ( – 2, – 1), B (1, 0), C (p, 3) and D (1, q) form a parallelogram ABCD, find the values of p and q.
If two vertices of a parallelogram are (3, 2) ( – 1, 0) and its diagonals meet at (2, – 5), find the other two vertices of the parallelogram
Find the coordinates of the vertices of the triangle the middle points of whose sides are \left(0, \frac{1}{2}\right) , \left( \frac{1}{2} , \frac{1}{2}\right)\text{ and }\left( \frac{1}{2}, 0\right).
Find the value of p for which the points ( – 5, 1), (1, p) and (4, – 2) are collinear.
Show by section formula that the points (3, – 2), (5, 2) and (8, 8) are collinear.
A (10, 5), B (6, – 3) and C (2, 1) are the vertices of triangle ABC. L is the mid point of AB, M is the mid-point of AC.
Write down the co-ordinates of L and M. Show that LM = \frac{1}{2} BC.
If A ( – 4, 3) and B (8, – 6), in what ratio is the line joining AB, divided by the x-axis
Show that PQ = 1/3 BC
In what ratio does the point ( – 4, b) divide the line segment joining the points P (2, – 2), Q ( – 14, 6) ?
Hence find the value of b.
Two vertices of a triangle are (3, – 5) and ( – 7, 4). Find the third vertex given that the centroid is (2, – 1).
Find the co-ordinates of the centroid of a triangle whose vertices are A ( – 1, 3), B(1, – 1) and C (5, 1)
Three consecutive vertices of a parallelogram ABCD are A (1, 2), B (1, 0) and C (4, 0).
Find the fourth vertex D.
The co-ordinates of two points A and B are ( – 3, 3) and (12, – 7) respectively. P is a point on the line segment AB such that AP : PB = 2 : 3.
Find the co-ordinates of P.
Prove that the points A ( – 5, 4), B ( – 1, – 2) and C (5, 2) are the vertices of an isosceles right angled triangle.
Find the co-ordinates of D so that ABCD is a square.
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