Today is our topic of discussion Coordinate geometry exercises 11-2 .
Coordinate geometry exercises 11-2
1. A(-2,0), B(5,0) and C(1, 4) are respectively the vertices of ΔABC.
1) Find the lengths of the sides AB, BC, CA and the perimeter of ΔABC.
2) Find the area of the triangles.
2. In each case find the area of the triangle ABC:
1) A(2,3), B(5, 6) and C(-1,4)
2) A(5, 2), B(1, 6) and C(-2,-3)
3. Show that the points A(1, 1), B(4, 4), C(4,8) and D(1, 5) are the vertices of a parallelogram. Find the lengths of the sides AC and BD. Find the area of the parallelogram using area of triangle upto three places of decimals.
4. What is the area of the quadrilateral ABCD with the vertices A(-a,0), B(0,-a), C(a, 0) and D(0, a)?
5. Show that the four points A(0, -1), B(−2,3), C(6, 7) and D(8,3) are the vertices of a rectangle. Find the lengths of its diagonals and the area of the rectangle.
6. If AB BC holds for the coordinates cf the three points respectively A(-2,1), B(10,6) and C(a,−6), find the possible value of a. Then find the area of the triangle formed with the help of the value of a.
7. The coordinates of the three points A, B, C are respectively A(a, a + 1), B(-6,-3) and C(5, -1). If the length of AB is twice of AC, find the possible value of a and describe the properties of the triangle ABC.
8. Find the area of the quadrilaterals as follows. [Use method no. 2]:
1) (0,0), (-2,4), (6,4), (4, 1)
2) (1,4), (4,3), (1, −2), (4,0)
3) (0,1), (-3, -3), (4,3), (5, 1)
9. Show that the the area of the polygon with vertices A(2,-3), B(3,-1), C(2,0), D(-1, 1) and E(-2, -1) is 11 square unit.
10. The vertices of a quadrilateral, arranged in anti-clockwise order, A(3, 4), B(-4,2), C(6, -1) and D(p, 3). Find the value of p if the area of the quadrilateral ABCD is twice the area of the triangle ABC.
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