Distance Formula

Q.

The points on X-axis at a distance of 10 units from (11, –8) are

1. (5, 0) and (16, 0)
2. (6, 0) and (17, 0)
3. (5, 0) and (17, 0)
4. (5, 2) and (17, 0)

Q.

The three vertices of a parallelogram taken in order are (–1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex

Q.

The two opposite vertices of a square are (–1, 2) and (3, 2). Find the co-ordinates of the other two vertices.

1. B (1, 0) or B ( 1, 4) and D(2, 4) or D(2, 0)
2. B (2, 3) or B ( 2, 4) and D(3, 4) or D(3, 0)
3. B (2, 0) or B ( 1, 4) and D(2, 4) or D(1, 0)
4. B (0, 1) or B (0, 2) and D(3, 1) or D(3, -2)

Q.

if A=5+ 2 root 6 find the value of rootA + 1/root A

Q.

The circle ${\mathrm{x}}^2+{\mathrm{y}}^2+4\mathrm{x}-4\mathrm{y}+4=0$ touches

1. $x-axis$

2. $y-axis$

3. $x-axisandy-axis$

4. None of These

Q.

Find the coordinates of the point equidistant from points $A(1,2),B(3,-4)$, and $C(5,-6)$.

Q.

What type of a quadrilateral do the points $A(2,-2),B(7,3),C(11,-1)$ and $D(6,-6)$ taken in that order, form?

Q.

The points on Y-axis at a distance of 13 units from point (–5, 7) are

1. (0, 5) (0, 19)
2. (0, 5) (0, –19)
3. (0, –5) (0, –19)
4. (0, –5) (0, 19)

Q.

The points (a, a) (–a, -a) and $(–\sqrt{3}a,\sqrt{3}a)$ form the vertices of an

1. Right angled triangle

2. Isosceles Right angled triangle

3. Equilateral triangle

4. Scalene triangle

Q.

State true or false.
The distance of any point (x, y) from the origin is (x+y) units.

1. True

2. False

Q.

If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus.

Q.

The distance of the point (-5, -5) from the origin is ___.

1. 5√2 units

2. √50 units

3. 
   2√5 units

4. √20 units

Q. Question 10
The point which lies on the perpendicular bisector of a line segment joining points A(-2, -5) and B(2, 5) is
(A) (0, 0)
(B) (0, 2)
(C) (2, 0)
(D) (–2, 0)

Q.

The $x$ axis, $y$ axis and a line passing through the point $A(6,0)$ form a $△ABC$. If $\angle A=30°$, then the area (in $sq\mathrm{units}$) of the triangle, is

1. $6\sqrt{3}$

2. $12\sqrt{3}$

3. $4\sqrt{3}$

4. $8\sqrt{3}$

Q.

The distance between the points (1, 3) and (5, 6) is ___ units.

Q. triangle ABC has vertices A(-4, 1) , B(2, -1) and C(1, K) The number of possible values of k such that triangle ABC is isosceles is ?

Q.

A point on the y-axis, whose distances from the points A(6, 7) and B(4, -3) are in the ratio 1 : 2 is__________.

1. (9, 0) or (0, $\frac{35}{3}$)

2. (0, 9) or (0, $\frac{-35}{3}$)

3. (0, 9) or (0, $\frac{35}{3}$)

4. (0, -9) or (0, $\frac{35}{3}$)

Q.

The area of a triangle is 5 square units. Two of its vertices are (2, 1) and (3, -2) and the third vertex lies on y = x + 3, the third vertex is

1. $(3,4)$

2. $(\frac{5}{2}$, $\frac{13}{2})$

3. $(\frac{7}{2}$, $\frac{13}{2})$

4. $(\frac{-3}{2}$, $\frac{3}{2})$

Q.

What is the distance between two points?

Q.

The distance between the points $(acos{25}^{\circ },0)$ and $(0,acos{65}^{\circ })$ is ___.

1. $acos{35}^{\circ }$

2. $2\sqrt{a}$

3. $a$

4. $0.5a$

Q.

The distance of the point (–2, –2) from the origin is

1. 2√2

2. 8

3. √2

4. √9

Q. The centre of a circle is (2x-1, 3x+1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit

Q.

State True or False.
Displacement is the shortest distance between the initial and final positions of the object.

1. True

2. False

Q. The points on the y-axis which are at a distance of 5 units from (4, -1) are

1. $(0,-2),(0,4)$
2. $(0,2),(0,4)$
3. $(0,2),(0,-4)$
4. $(0,-2),(0,-4)$

Q.

The ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis is

1. $6:5$

2. $3:5$

3. $7:2$

4. $5:2$

Q.

Find the distance between the points (-3, -3) and (4, 5).

1. $\sqrt{111}$

2. $\sqrt{131}$

3. $\sqrt{112}$

4. $\sqrt{113}$

Q.

The point (1, –3), (13, 9), (10, 12) and (–2, 0) taken in order form the vertices of _________________

1. Square
2. Rectangle
3. Rhombus
4. Triangle

Q.

The points (2, –1), (3, 4), (–2, 3) and (–3, –2) taken in the order from the vertices of _________________

1. Square
2. Rhombus
3. Rectangle
4. Triangle

Q. What are the coordinates of the point E and F of the given below graph?

Q. A (-1, 1), B (1, 3) and C (3, a) are points and if AB = BC, then find ‘a’

1. 5
2. 6
3. 8
4. 7