Distance between two points using Pythagoras theorem

Q. The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is

1. Scalene
2. Equilateral
3. None of these
4. Isosceles

Q. Assertion: Points A(6, 4), B(-4, -6) and C(4, 6) are such that AB =$\sqrt{200}$, BC= $\sqrt{208}$, AC= $\sqrt{8}$, Since AB+BC>AC, points A, B and C from a triangle.

Reason: If $B{C}^2=A{B}^2+A{C}^2$, then $\Delta ABC$ is a right triangle, right angled at A.

1. If both assertion and reason are true but reason is not the correct explanation of assertion.
2. If assertion is true but reason is false.
3. If assertion is false but reason is true.
4. If both assertion and reason are true and reason is te correct explanation of assertion

Q. A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the point B if AB and BC are parallel to the coordinate axes.

1. (2, 1)
2. (3, 2)
3. (5, 4)
4. (1, 1)

Q.

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Find the length of the ladder.

__

Q.

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median, AB = 8 cm and BC = 6 cm. Then, choose the correct option(s).

1. MC = 5 cm

2. AM = 5 cm

3. MB = 5 cm

4. AC = 5 cm

Q.

List-II gives distance between pair of points given in List-I, match them correctly.
$\begin{array}{cccc}& List-I& & ListII\\ \left(P\right)& (-5,7),(-1,3)& \left(1\right)& 5\\ \left(Q\right)& (5,6),(1,3)& \left(2\right)& \sqrt{8}\\ \left(R\right)& (\sqrt{3}+1,1),(0,\sqrt{3})& \left(3\right)& \sqrt{6}\\ \left(S\right)& (0,0),(-\sqrt{3},\sqrt{3})& \left(4\right)& 4\sqrt{2}\end{array}$

1. P-4, Q-1, R-2, S-3

2. P-3, Q-2, R-4, S-1

3. P-1, Q-2, R-3, S-4

4. P-4, Q-3, R-2, S-1

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. The distance of point P(x, y) from the origin is $=\sqrt{x^2+y^2}$

1. True
2. False

Q.

The length of the hypotenuse in the figure is:

1. 6

2. 5

3. 4

4. 3

Q.

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

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

2. $a$

3. $0.5a$

4. $2\sqrt{a}$