# Distance Formula

## Trending Questions

**Q.**

The equation of the locus of a point whose distance from (*a*, 0) is equal to its distance from *y*-axis, is

**Q.**

The distance between the points P(1, –3, 4) and Q (– 4, 1, 2) is:

√5 units

5 units

2√13 units

3√5units

**Q.**

The equation to the locus of a point which moves so that its distance from x-axis is always one half its distance from the origin, is

x2+3y2=0

x2−3y2=0

3x2+y2=0

3x2−y2=0

**Q.**

Locus of the points which are at equal distance from $3x+4y-11=0$ and $12x+5y+2=0$ and which is near the origin is

$21x\u201377y+153=0$

$99x+77y\u2013133=0$

$7x\u201311y=19$

None of these

**Q.**Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.

**Q.**

If vertices of a quadrilateral are *A* (0, 0), *B*(3, 4), *C*(7, 7) and *D*(4, 3) then quadrilateral *ABCD* is

Parallelogram

Rectangle

Rhombus

Square

**Q.**

The points (3*a*, 0), (0, 3*b*) and (*a*, 2*b*) are

Vertices of an equilateral triangle

Vertices of an isosceles triangle

Vertices of a right angled isosceles triangle

Collinear

**Q.**

A point moves in such a way that the sum of square of its distance from the points A(2, 0) and B(-2, 0) is always

equal to the square of the distance between A and B. The locus of the point is

**Q.**

The coordinates of a point which is equidistant from the points (0, 0, 0), (a, 0, 0), (0, b, 0)and(0, 0, c) are given by _____

**Q.**Show that the points A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6) form an isosceles right-angled triangle.

**Q.**Show that x^2 - 7x - 14(q^2 +1) =0 (q belongs to integers) has no integral root.

**Q.**If P(1+t√2, 2+t√2) be any point on a line, then the range of values of t for which the point P lies between the parallel lines x + 2y = 1 and 2x + 4y = 15, is

**Q.**The distance of the point (1, 2) from the line 3x+4y–5=0 is

- 65
- 56
- 165

**Q.**

The points A(−2, 3, 5), B(1, 2, 3)andC(7, 0, −1) are _____

Collinear

Vertex of equilateral triangle

vertex of right angled isosceles triangle

vertex of right angle triangle

**Q.**

Find the length of the medians of the triangle with vertices A(0, 0, 6) B(0, 4, 0) and C(6, 0, 0).

**Q.**

Three students are standing in a park with signboards 'SAVE ENVIRONMENT', 'DON'T LITTER' and 'KEEP YOUR PLACE CLEAN'. Their positions are marked by the points A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6).

Three students are holdings green colour ribbon together. Does the ribbons form sides or a right angled triangle? Do you feel the need to promote?

What message is given from this question to the society?

**Q.**Show that the points A(0, 1, 2), B(2, -1, 3) and C(1, -3, 1) are vertices of an isosceles right angled triangle.

**Q.**

Find the coordinates of a point on y-axis which are at a distance of 5√2 from the point P(3, −2, 5).

**Q.**

**Find the value of **$a$**, if the distance between the points **$A(-3,-14)$** and **$B(a,-5)$** is **$9$** units.**

**Q.**

The distance of (2, 3) from x+y=1 is

2 units

2√2 units

4√2 units

3√2 units

**Q.**

If A(z1), B(z2), C(z3) be the vertices of triangle ABC in which |ABC–––––– = π4 and ABBC = √2 then z2 is equal to

**Q.**

The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope √3 is

**Q.**

Find the equation of the circle passing through the points (4, 1) and (6, 5) whose centre is on the line 4x + y = 16.

or

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of locus of point P on the rod, which is 3 cm from the end in contact with the X-axis.

**Q.**Find the point in yz-plane which is equidistant from the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).

**Q.**

The distance between the pair of points (7, 8) and (4, 2), if origin gets shifted to (1, -2), would be _________

45

3√5

√157

3√3

**Q.**

If z lies on the curve |z| = 1 such that a ≤ |z+1| + |1 + z2 - z| ≤ b then (a, b) can be

(1 , 3)

**Q.**

The equation of locus of a point where distance from the y-axis is equal to its distance from the point A(2, 1, -1) is-

x2+y2+z2=6

x2−4x+2z+6=0

x2+y2−z2=0

y2−2y−4x+2z+6=0

**Q.**If the vertices of A, B, C of a triangle ABC have position vectors (1, 2, 3), (-1, 0, 0) and (0, 1, 2) respectively then angle ABC equals

**Q.**distance between the points A(0, 7, 10) and C(–4, 9, 6) in space is

- 4
- 5
- 6
- 8

**Q.**

A birdlover at p(x, y, z) from a house watches two birds sitting on the branches of another tree at A(2, 5, 8) and B(3, 7, 2) such that AP=BP , show that 2x+4y−2z+31=0