Distance between Two Points Using Pythagoras Theorem

Q. A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the ladder from base of the wall.

1. $6m$
2. $8m$
3. $6.5m$
4. $7m$

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

1. False
2. True

Q.

A ladder $5m$long when set against the wall of a house, just reaches a window at a height of $4m$. How far is the foot of the ladder from the wall?

Q.

What is the perpendicular distance between the line x = 4 and the point M (2, 1)

1. $\frac{1}{2}$units
2. 2 units
3. $\sqrt{2}$ units
4. 4 units

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. Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right triangle.

Q. In the given figure, $\angle ABC=90°$ and BM is a median, AB = 8 cm and BC = 6 cm. Then, find BM

Q. In $\Delta$ABC, if AB = 7 cm and BC = 6 cm, which of the following is true?.

1. 5 cm < AC < 11 cm
2. 1 cm < AC < 13 cm
3. 1 cm < AC < 10 cm
4. 2 cm < AC < 12 cm

Q.

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

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

2. $0.5a$

3. $2\sqrt{a}$

4. $a$

Q.

What is the perpendicular distance between the line x = 4 and the point M (2, 1)

1. 4 units
2. $\frac{1}{2}$units
3. $\sqrt{2}$ units
4. 2 units

Q. What are the coordinates of a point which lies on the x-axis at a distance of 5 units from y-axis?

Q.

The length of the hypotenuse in the figure is.

1. 13
2. 5
3. 12

Q.

D, E F are the midpoints of the sides AB, BC CA of an isoscels triangle ABC in which AB=BC. prove that the triangle DEF is also an isoscels triangle.

Q. In triangle ABC, if A =x, B = y, and c =z such that x = 4y/3 and y= 3z/8, then B is equal to

Q.

What is the perpendicular distance between the line x = 4 and the point M (2, 1)

1. $\frac{1}{2}$units
2. $\sqrt{2}$ units
3. 2 units
4. 4 units

Q.

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.