Distance Formula

Q.

Find a point on the x-axis which is equidistant from the points $(7,6)$ and $(-3,4)$.

Q.

An equilateral triangle has two vertices at the points (3, 4) and (-2, 3), find the coordinates of the third vertex.

Q. Find the distance of a point P(x, y) from the origin.

Q.

The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.

1. $2\sqrt{b^2+c^2}$

2. $2\sqrt{2}b$

3. $2\sqrt{a^2-c^2}$

4. $2\sqrt{a^2+b^2}$

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. (1, 9)

2. (5/2, 13/2)

3. (7/2, 13/2)

4. (3, 4)

Q. Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distance covered area ins straight lines). If the house is situated at (2, 4), bank at(5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.

1. 27km
2. 2.4km
3. 24.6 km
4. 1.6km

Q. Find the value of k , if the point P (0, 2) is equidistant from (3, k ) and (k, 5) .

Q.

The distance between the points (a, b) and (– a, – b) is:

1. a² + b²

2. √(a² + b²)

3. 2√(a² + b²)

4. 0

Q.

The centre of a circle is (2a, a-7). Find the values of a if the circle passes through the point (11, -9) and has diameter $10\sqrt{2}units.$

Q. Find the coordinates of a point P, which lies on the line segment joining the points A (− 2, − 2) and B (2, − 4) such that $\mathrm{AP}=\frac{3}{7}\mathrm{AB}$

Q.

Displacement is the shortest distance between the initial and final positions of the object.

1. True
2. False

Q. Question 16
If a circle drawn with origin as the centre, passes through $(\frac{13}{2},0)$, then the point which does not lie in the interior of the circle is
(A) $(\frac{-3}{4},1)$
(B) $(2,\frac{7}{3},)$
(C) $(5,\frac{-1}{2})$
(D) $(-6,\frac{5}{2})$

Q.

The distance between the points $(cos\theta ,sin\theta )$ and $(sin\theta ,-cos\theta )$ is

1. $\sqrt{2}$

2. 2

3. 1

4. $\sqrt{3}$

Q.

Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).

Q.

If the points A(4, 3) and B(x, 5) lie on the circle with centre O(2, 3), find the value of x.

Q. Prove that the points $(3,0),(6,4)$ and $(-1,3)$ are the vertices of a right angled isosceles triangle.

Q. Question 9
If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

Q. Question 5
If AOBC is a rectangle whose three vertices are A(0, 3), 0(0, 0) and B(5, 0), then the length of its diagonal is:
(A) 5
(B) 3
(C) $\sqrt{34}$
(D) 4

Q.

If any point $\text{P}$ is at the equal distances from points $\text{A (a + b, a - b)}$and $\text{B (a - b, a + b),}$ then locus of point $\text{P}$ is

1. $\text{x – y = 0}$

2. $\text{ax + by = 0}$

3. $\text{bx + ay = 0}$

4. $\text{x + y = 0}$

Q.

If the distance between the points (4, p) and (1, 0) is 5, then p = ___

1. $\pm 4$

2. $\pm 2$

3. $\pm 2\sqrt{2}$

4. $\pm 4\sqrt{2}$

Q. Centre of the circle passing through the points (6, -6), (3, -7) and (3, 3) is .

1. (3 , 2)
2. (2 , 3)
3. (3 , -2)

Q.

Displacement of a body can be zero even when the distance travelled is not zero. Explain.

Q.

The in-centre of the triangle with vertices $\left(1,\sqrt{3}\right)$, $\left(0,0\right)$ and $\left(2,0\right)$ is

1. $\left(1,\frac{\sqrt{3}}{2}\right)$

2. $\left(\frac{2}{3},\frac{1}{\sqrt{3}}\right)$

3. $\left(\frac{2}{3},\frac{\sqrt{3}}{2}\right)$

4. $\left(1,\frac{1}{\sqrt{3}}\right)$

Q.

Find the distance between the points $(\frac{-8}{5},2)and\left(\frac{2}{5}2\right)$

Q.

Prove that (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.

Q. What is the distance of the point (3, 5) from the y axis?

1. 8 units
2. 5 units
3. 3 units
4. 2 units

Q.

Which point on y-axis is equidistant from (2, 3) and (-4, 1) ?

Q.

Find the coordinates of the point equidistant from three given points A(5, 3), B(5, -5) and C(1, -5).

Q. Question 7
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

Q.

Find the point on x- axis which is equidistant from the points (-2, 5) and (2, -3).