A) FILL THE BLANKS:
a) If a point lies on x-axis, then y coordinate is_____
b) If a point lies on y-axis, then x coordinate is ____.
c) If two points have same abscissa, the line joining them is parallel to____.
d) If two points have same ordinate, the line them is parallel to_____.
e) The line joining (2,3) and (-2,-3) passes through the_____.
1) Find the distance between:
a) (-2,3), (6.9). 10 units
b) (5, 18),(-4, -22). 41 units
c) (-7, -24),(0,0). 25 units
d) (2/5, 2/5), (-2/5,-1/5). 1 unit
e) (5/10, 1/10),(-1/10,-7/10). 1
f) (√3,1),(0,0). 2
g) (-2,3),(6,-3). 10
h) (2,3),(-2,3). 4 units
i) (3,5),(3,1). 4 units
j) (2,-2),(5,2). 5 units
k) (3,7),(-2, -5). 13 units
2) Find:
a) A is a point on the Y-axis whose ordinate is 5 and B is the point (-3,1). Calculate the length of AB. 5 units
b) The distance between A (1,3) and B(x,7) is 5. Find x. 4 or -2
c) Calculate the distance between A(7,3) and B on the x-axis whose abscissa is 11. 5
d) Find the coordinates of the points on the y-axis Which are at a distance of 13 units from the points (12,9). (0,4),(0,14)
e) Find the coordinates of the points on the x-axis Which are at a distance of 5 units from the points (5,4). (8,0),(2,0)
f) What point/s on the Y-axis are at a distance of 10 units from the point (8,8), (0,2). (0,14)
g) Find point/s which are at a distance of √10 from the point (4,3), given that the ordinate of the point/s is twice the abscissa.
(1,2)
h) A point P is at a distance of √10 units from the point (4,3). Find the coordinate of P, it being given that its ordinate is twice its abscissa. (3,6),(1,2)
i) If A is (4,2) and B(1,y), find the possible values of y so that AB= 5. -2, 6
3)
a) Show that the point (4,4) is equidistant from the points A(1,0) and B(-1,4).
b) What point on the x-axis is equidistant from A(5,4), B(-2,3). (2,0)
c) Find a point equidistant from the points A(6,2), B(-1,3), and C(-3, -1). (2,-1)
d) If A is (2,5) and B is (x, -7), find the possible values of x so that AB= 13. -3, 7
e) What points on the x-axis are at a distance of 17 units from the point A(11,-8). (26,0) and (-4,0)
f) What points on the y-axis are at a distance of 10 units from the point A(-8, 4). (0,10) and(0,2)
4) show that the points form a right angled triangle ::
a) A(6,6), B(2,3), C(4,7).
b) A(60), B(-2,6), C(12,8).
c) A(0,3), B(-2,1), C(-1,4).
d) A(-3,-4), B(2,6), C(-6,10).
e) A(3,3), B(9,0), C(12,21).
5) Show that the points form an equilateral triangle..
a) A(1,1), B(-1,-1), C(-√3,√3).
b) A(2a, 4a),B(2a, 6a),C(2a +√3a, 5a).
6) Show that the points form an isosceles right angled triangle.
a) A(7,10), B(-2, 5), C(3, 4).
7) Show that the given points are collinear:
a) A(-2,3), B(1,2), C(7,0)
b) (3, -2), B(5,2), C(8,8)
c) A(1, 1), B(--2, 7), C(3,-3).
d) (-1,-1), B(2, 3), C(8, 11).
8) If A(7,5), B(2,4) and C(6,10), show that AB= AC. Assign special name to the triangle ABC. Isosceles triangle
9) Show that Isosceles triangle
a) A(2,-4), B(7,-1), C(5, 1).
10) Find the circumference of the triangle whose vertices are (-2,-3), (-1,0), (7, -6). (3,-3)
11) Show that P(11,2) is the centre of the circle which passes through A(1,2), B(3,-4), C(5, -6).
12) The centre of a circle is (x+2, x-1). Find x if the circle passes through (2,-2),,(8,-2).. 3
13) Show that the points are the vertices of a rectangle.
a) (2,-2),(8,4),(5,7),(-1,1)
14) Show that the points form rhombus..
a) A(7,3), B(3,0), C(0,-4) (4, -1).
b) A(0,5), B(-2,-2), C(5,0) (7, 7)
15) Prove for Parallelogram:
a) A(1,2), B(-2,-1), C(1,0) (4, 3).
16) Find a if the triangle formed by A(8,10), B(7, -3), C(0, a) is right angled at B. -4
17) Show that it is square:
a) (2,1), B(0,3), C(-2,1) (0, -1).
No comments:
Post a Comment