Nootan solutions for माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 11 - Section formula [Latest edition]

Find the coordinates of the mid-point of the line segment joining the following points:

(12, 5) and (2, 7)

Find the co-ordinates of the mid-point of the line segment joining the following points:

(−2, −4) and (−3, 2)

Find the co-ordinates of the mid-point of the line segment joining the following points:

(−3, 5) and (3, −5)

Find the co-ordinates of a point R which divides the line segment joining the points P(−2, 3) and Q(4, 7) internally in the ratio 4:7.

Find the co-ordinates of the point P which divides the line segment joining A (−3, 3) and B (2, −7) internally in the ratio 2 : 3.

Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.

Determine the ratio in which the point M (k, 1) divides the line segment joining the points A (7, −2) and B (−5, 6). Also, find the value of K.

Show that the mid-point of line segment joining the points (0, 5) and (15, 7) is same as the mid-point of line segment joining the points (8, −15) and (7, 27).

Find the ratio in which the line segment joining the following points is divided by the X-axis:

(5, 4), (1, −3)

Find the ratio in which the line segment joining the following points is divided by the X-axis:

(6, −4), (5, 5)

Find the ratio in which the line segment joining the following points is divided by the X-axis:

(3, −2), (2, 3)

Find the ratio in which the line segment joining the points (−2, 5) and (3, 7) is divided by the Y-axis.

Find the distance of point (0, 0) from the mid-point of the line segment joining the points (5, −5) and (11, 17).

Find the lengths of medians of a triangle whose vertices are (3, −6), (7, 4), and (−5, 2).

The line segment joining the points (3, −1) and (−6, 5) is trisected. Find the co-ordinates of the points of trisection.

Find the co-ordinates of the points dividing the line segment joining the points (−3, 5) and (5, 1) into four equal parts.

The co-ordinates of the points P and Q are (3, y) and (x, 5), and the co-ordinates of the mid-point of line segment PQ are (2, 4). Find the values of x and y.

P (1, −2) is a point on the line segment joining points A (3, −6) and B (x, y). If P divides AB in the ratio 2 : 3, find the coordination of B.

Prove that the points (2, −3), (6, 7), (8, 3), and (4, −7), taken in order, are the vertices of a parallelogram.

Find the 4^th vertex of a parallelogram if three vertices taken in order are (−5, −5) (2, −3), and (4, 4).

Find the 4^th vertex of a parallelogram if three vertices taken in order are (1, −1), (−2, 2), and (4, 8).

If the points A (6, 2), B (2, k), С (1, 5), and D (5, 6), taken in order, are the vertices of a parallelogram, find the value of k.

The coordinates of one end point of a diameter of a circle are (3, 5). If the co-ordinates of the centre be (6, 6), find the co-ordinates of the other end of the diameter.

The endpoints of a diameter of a circle are (−5, −2) and (−2, −6). Find the co-ordinates of the centre and radius of the circle.

A (−2, 3) and B (3, −1) are two vertices of a paralļelogram ABCD. Its diagonals interested each other at point (1, 5), find the co-ordinates of C and D.

Find the co-ordinates of the centroid of a triangle whose vertices are (4, 0), (2, 3), and (0, 0).

The co-ordinates of the centroid of a triangle are (2, −5). If two of its vertices are (−6, 5) and (11, 8), find the coordinates of the third vertex.

The co-ordinates of the vertices of a triangle are (3, 1), (b, 4), and (1, a), and its centroid is (3, 4). Find the values of a and b.

Find the vertices of a triangle, the mid-points of whose sides are (−1, 2), (−2, 6), and (4, −1).

Find the vertices of a triangle, the mid-points of whose sides are (1, 2), (3, 4), and (2, 2).

Find the lengths of the medians of a triangle whose vertices are A (−1, 3), B (1, −1), and C (5, 1).

The mid-point of the line segment AB shown in adjoining figure is (5, −4). Find the co-ordinates of A and B.

In what ratio does the line x − y = 2 divides the line segment joining the points (3, −1) and (8, 9)? Also, find the coordinates of the point of division.

The coordinates of the vertices of ΔABC are respectively (–4, –2), (6, 2), and (4, 6). The centroid G of ΔABC is ______.

(a, b) is the mid-point of the line segment joining the point A (10, −6) and B (k, 4), and 3a − 2b = 26, then the value of k is ______.

The co-ordinates of a point which divides the line segment joining the points (3, 5) and (8, 10) in the ratio 2 : 3, are ______.

Point M lies on the line segment joining the points A(6, 0) and B(0, 8) such that AM : BM = 2 : 3, the coordinates of point M are ______.

The ratio in which the point (m, −6) divides the line segment joining the points (−1, −3), and (9, −8) is ______.

The ratio in which the Y-axis divides the line segment joining the points (2, 1) and (−3, −5) is ______.

The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are ______.

The co-ordinates of the vertices of ΔABC are A(3, 1), B(1, 6) and C(5, 4). The length of median through A is ______.

The coordinates of one end point of a diameter of a circle are (5, 2). If the coordinates of its centre are (2, 3), then the coordinates of the other end of diameter are ______.

The mid-point of the line segment joining (2k, 6) and (−4, −2) is (3, 2). The value of k is ______.

Assertion: The coordinates of A and B are (1, 2) and (2, 3), respectively. If R is a point on AB such that AR : RB = 4 : 3, then coordinates of R will be `(11/7,  18/7)`.

Reason: The coordinates of the mid-point of line segment joining (x₁, y₁) and (x₂, y₂) are `((x_1 + x_2)/2, (y_1 + y_2)/2)`.

Assertion: The ratio in which the point (−6, a) divides the join of (3, −1) and (−8, 9) is 3 : 2.

Reason: The diagonals of a parallelogram do not bisect each other.

Assertion: The coordinates of the vertices of a triangle are (1, 1), (2, 5), and (3, 0). The coordinates of its centroid are (1, 2).

Reason: The coordinates of the centroid of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) are `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`.

Assertion: The endpoints of a diameter of a circle are (3, −5) and (1, 1). Its centre will be (2, −2).

Reason: The coordinates of the mid-point of line segment joining (x₁, y₁) and (x₂, y₂) are `((x_1 + x_2)/2, (y_1 + y_2)/2)`.

1. The mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).
2. The diagonals of a rectangle are equal and bisect each other.

1. The distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4) is 5 units.
2. y-axis divides the line segment joining A(−4, 6) and B(8, −3) in the ratio 2 : 1.

1. x-axis divides the line segment joining points (6, 4) and (1, −3) in the ratio 1 : 1.
2. If the points A (6, 1), В (8, 2), С (9, 4), and D (p, 3), taken in order, are the vertices of a parallelogram, then p = 7.

1. The ratio in which the line 2x + y = 4 divides the line segment joining A (2, −2) and B (3, 7) is 2 : 5.
2. G (4, 3) is the centroid of ΔABC, where A (1, 3), В (4, b), and C (9, 1), then b = 4.