Distance between Two Points

Q. The distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. $\sqrt{(x_2+x_1{)}^2+(y_2+y_1{)}^2}$
2. $\sqrt{(x_2-x_1{)}^2+(y_2+y_1{)}^2}$
3. $\sqrt{(x_2+x_1{)}^2+(y_2-y_1{)}^2}$
4. $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Q.
What is the distance between the point (3, 4) and the origin?

1. 4 Units
2. 5 Units
3. 6 Units
4. 7 Units

Q. The Pythagorean Theorem can be used to find the distance betwen any to points on the Cartesian plane.

1. True
2. False

Q. Find a relation between $a$ and $b$ such that the point $(a,b)$ is equidistant from the points $(1,1)$ and $(7,9).$

1. $4a+3b=32$
2. $3a+4b=32$
3. $a+b=10$
4. $a-b=32$

Q.
What is the distance between points $(0,2)$ and $(3,2)$?

1. $1$ Unit
2. $2$ Units
3. $3$ Units
4. $4$ Units

Q. Find the distance between the points $(-1,6)$ and $(2,2).$

1. $\text{3 units}$
2. $\text{4 units}$
3. $\text{5 units}$
4. $\text{6 units}$

Q. The distance 'd' between any two random points on the Cartesian plane $A(x_1,y_1)andB(x_2,y_2)$is:

1. $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
2. $\sqrt{{(x_2-x_1)}^2-{(y_2-y_1)}^2}$
3. $\sqrt{{(x_2+x_1)}^2+{(y_2+y_1)}^2}$
4. $\sqrt{{(x+x_1)}^2-{(y_2+y_1)}^2}$

Q. Jack started from the home (1, 1) and moved 8 units on the x-axis and 6 units on the y-axis to reach his office. Find the distance between home and office.
units

Q.
The distance between the points $(2,2)$ and $(-2,-2)$ is units.

1. $3\sqrt{2}$
2. $4\sqrt{2}$
3. $4$
4. $6$

Q. What is the value of c, if the point $(c,c)$ is at a distance of $\sqrt{18}$ units from the origin?

1. c = +3
2. c = -3
3. c = ±3

Q.
What is the distance between the points $(2,-3)$ and $(2,0)$?

1. $2$ Units
2. $3$ Units
3. $4$ Units
4. $5$ Units

Q. The Possible value(s) of $a$ such that, the distance between the points $(2,3)$ and $(a,4)$ is equal to $\sqrt{17}$ units is/are:

1. $-6$
2. $2$
3. $-2$
4. $6$

Q. Match the following points to the distances between them.

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

Q. Select the correct option about generalizing the rule for rotating a point (x, y) about the origin in the counterclockwise direction at a certain angle.

1. For a rotation of 270°,
   $(x,y)\to (y,-x)$
2. All the above statements are correct
3. For a rotation of 180°,
   $(x,y)\to (-x,-y)$
4. For a rotation of 90°,
   $(x,y)\to (-y,x)$

Q. What is the distance between the points $(2,3)$ and $(8,-5)?$

1. $8$ units
2. $10$ units
3. $12$ units
4. $14$ units