Distance between Two Points

Q. In the given figure , Find the distance AB.

1. 4 units
2. 2 units
3. 1 unit
4. 3 units

Q.

The points $(2,5)$ and $(5,1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y=2x+k$, then the value of $k$ will be

1. $4$

2. $3$

3. $-4$

4. $-3$

Q. The point (2, 3) lies in the __________.

1. $1^{st}$ Quadrant
2. $2^{nd}$ Quadrant
3. $3^{rd}$ Quadrant
4. $4^{th}$ Quadrant

Q.

If point P lies on the line y = 2, then what is its x-coordinate?

1. 2

2. -2

3. 0

4. Cannot be determined

Q.

Write whether the following statements are True or False? Justify your answer. Point $(3,0)$lies in the first quadrant.

1. True
2. False

Q.

If the midpoint of join of $(x,y+1)$ and $(x+1,y+2)$ is $\left(\frac{3}{2},\frac{5}{2}\right)$ then the midpoint of join of $(x-1,y+1)$ and $(x+1,y-1)$ is

1. $\left(-1,-1\right)$

2. $\left(1,1\right)$

3. $\left(1,-1\right)$

4. $\left(-1,1\right)$

Q. Determine ‘𝒙’ so that 𝟐 is the slope of the line through 𝑷(𝟐, 𝟓) and 𝑸(𝒙, 𝟑).

Q. If (7, 3), (6, 1), (8, 2) and (p, q) are the vertices of a parallelogram, taken in order, then the value of p is

1. 9

Q.

Which of the lines represents the perpendicular distance from point A (2, 3) to line l, x =4

1. AB

2. AC

3. AD

4. DA

Q. $(3,0)$ is a point on the line joining the points $(3x^2,6x)$ and $(3y^2,6y)$. Then the value of $xy=$.

1. -1
2. 2
3. 1

Q. Find the points on the y-axis, each of which is at a distance of 13 units from the point (-5, 7).

Q. In the given figure points A and B lie on the X axis. Find the distance AB.

1. 2.5 units
2. 3 units
3. 1 units
4. 2 units

Q. In the given figure, the Distance D(P, Q) is:

1. $y_1+y_2$
2. $y_2-y_1$
3. $y_1-y_2$
4. $y_1^2-y_2^2$

Q. Locate the given coordinates in the XY plane.

1. Quadrant II
2. on the Y-axis
3. on the X-axis
4. Quadrant III

Q.

If point P lies on the line y = 2, then what is its x-coordinate?

1. 2

2. -2

3. 0

4. Cannot be determined

Q. Using Pythagorean theorem, the distance between points (−𝟏, 𝟐) and (𝟐, 𝟔) is:

1. 50 cm

2. 25 cm

3. 5√2 cm

4. 5 cm

Q. The point (2, 0) lies in both the $1^{st}$ and $4^{th}$ quadrants.

1. True
2. False

Q.

If (7, 3), (6, 1), (8, 2) and (p, q) are the vertices of a parallelogram, taken in order, then find the values of p and q.
p = ___ and q = ___

1. p = 4, q = 9

2. p = 5, q = 6

3. p = 9, q = 6

4. p = 9, q = 4

Q. A point which lies on the X-axis has its Y-coordinate as __________.

1. 0
2. 1
3. y
4. None of the above

Q.

If the vertices of a rectangle are (0, 3), (0, 0), (4, 3) and (4, 0), the length of its diagonals is ____

1. 4

2. 8

3. 5

4. 6

Q.

The distance of any point $(x,y)$ from the origin is =

1. $x+y$

2. $\sqrt{x+y}$

3. $\sqrt{x^2+y^2}$
4. $\sqrt{x^2-y^2}$

Q. The point (2, 0) lies __________.

1. on the $2^{nd}$ Quadrant
2. on the Y-axis
3. on the $3^{rd}$ Quadrant
4. on the X-axis

Q.

What is the distance of the point (6, 18) from the X-axis?

1. 6

2. 4

3. 10

4. 18

Q.

What is the distance of the point (-6, 8) from the origin?

1. 20

2. 2

3. 10

4. 14

Q. State true or false. The point (2, 0) lies in both the $1^{st}$ and $4^{th}$ quadrants.

1. True
2. False

Q. Label the parts with their corresponding names.

1. ordinate
2. abscissa
3. origin
4. third quadrant

Q. Locate the given coordinates in the XY plane.

1. Quadrant II
2. on the Y-axis
3. on the X-axis
4. Quadrant III