exercise 7.2 co ordinate geometry chapter 7 cbse ncert 10th mathematics section formula , midpoint formula
10.Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order
take
A= (3, 0)
B=(4, 5)
C= (– 1, 4)
D=(– 2, – 1)
diagonals are AC and BD
A= (3, 0) =(x1,y1)
C= (– 1, 4)=(x2,y2)
using distance formula
AC= sqrt{(-1-3)^2 + (4-0)^2} =sqrt(32)=4sqrt(2)
B= (4,5) =(x1,y1)
D= (– 2, -1)=(x2,y2)
using distance formula
BD=sqrt{ (-2-4)^2 +(-1-5)^2 } =sqrt(72)=6sqrt(2)
area of a rhombus =(1/2)*AC*BD=24 sq.units
exercise 7.1 co ordinate geometry chapter 7 cbse ncert 10th mathematics distance formula, collinear points using distance formula
Find the distance between the following pairs of points :(2, 3), (4, 1)
(2,3) =(x1,y1)
(4,1))=(x2,y2)
using distance formula
distance = sqrt{(4-2)^2 +(1-3)^2} =sqrt(8) =2sqrt(2) units.
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ncert cbse 10th mathematics
co ordinate geometry chapter 7
exercise 7.4 optional exercise
Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).
2. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
3. Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).
4. The two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of the other two vertices.
6. The vertices of a ∆ ABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively so that [AD/AB] =[AE/AC] =[1/4] Calculate the area of ∆ ADE and compare it with the area of ∆ ABC
7. Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of ∆ ABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
8. ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and
D(5, – 1). P, Q, and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.
exercise 7.3
Find the area of the triangle whose vertices are
(2, 3), (–1, 0), (2, – 4)
(ii) (–5, –1), (3, –5), (5, 2)
2. In each of the following find the value of ‘k’, for which the points are collinear.
(7, –2), (5, 1), (3, k)
(ii) (8, 1), (k, – 4), (2, –5)
4. Find the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3).
exercise 7.2
10.Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order
9. Find the coordinates of the points which divide the line segment joining
A(– 2, 2) and B(2, 8) into four equal parts.
8. If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP =(3/7) AB and P lies on the line segment AB.
7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2,-3) and B is (1,4)
5. Find the ratio in which the
line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis.
Also find the coordinates of the point of division.
4.Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
2. Find the coordinates of the points of trisection of the line segment joining
(4, –1) and (-2,-3)
Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the
ratio 2 : 3
exercise 7.1
Find the distance between the following pairs of points :(2, 3), (4, 1)
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