Distance between Points Not Parallel to X & Y Coordinates

Q.

Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

Q. Distance between the points $(x_1,-y_1)and(-x_2,y_2)$ =.

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

Q. Distance between the points $(-x_1,-y_1)and(-x_2,-y_2)$ is given by

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

Q. From the figure, the distance between the points A(3, 4) and C(9, 4) is

1. 3
2. 4
3. 5
4. 6

Q. Question 1 (iii)
Find the distance between the following pairs of points:
(iii) (a, b), (− a, − b)

Q. The distance between the points $(x_1,-y_1)\text{and}(-x_2,y_2)$ is ___ units.

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.

M (-2, y) is a point equidistant from the coordinates A(5, 7) and B(3, -4). Find the value of y.

1. $\frac{36}{19}$
2. $\frac{47}{23}$
3. $\frac{57}{22}$
4. 2

Q. If the adjacent vertices of a square are (2, 5) and (6, 8), the area of the square is square units.

1. 16
2. 25
3. 30

Q. The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.

1. $2\sqrt{a^2+b^2}$
2. $2\sqrt{b^2+c^2}$
3. $2\sqrt{2}b$
4. $2\sqrt{a^2+c^2}$

Q. The distance between the points (5, 5) and (3, 3) is ___.

1. $2\text{units}$
2. $2\sqrt{2}\text{units}$
3. $\sqrt{2}\text{units}$
4. $8\sqrt{2}\text{units}$

Q. Distance between the points $(x_1,-y_1)and(-x_2,y_2)$ =.

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

Q.

The distance between A (1, 3) and B (x, 7) is 5. The value of x if x > 0 is :

1. 4
2. 2
3. 1
4. 3

Q.

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area. [3 MARKS]

Q.

Find the distance between the points (0 , 0) and (4, 0). ( 1 mark)

1. 5
2. 8
3. 6
4. 4

Q. Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (−5, 7), (−1, 3)

Q.

The distance between the points (5, 5) and (3, 3) is ___.

1. $2units$

2. $2\sqrt{2}units$

3. $\sqrt{2}units$

4. $8\sqrt{2}units$

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

1. 7 units
2. 8 units
3. 9 units
4. 10 units

Q.

If the distance between points (p, –5), (2, 7) is 13 units, then $p$ is _____________

1. –3 or 7
2. –7 or 3
3. –3 or –7
4. 3 or 7

Q.

Find the distance between the points (-3, -3), (4, 5). [2 MARKS]

Q. Question 1 (iii)
Find the distance between the following pairs of points:
(iii) (a, b), (− a, − b)

Q. If A(-3, 5), B(0, -4), C(6, -2), and D(3, 7), find the area of the rectangle ABCD.

1. 20 square units
2. 30 square units
3. 40 square units
4. 60 square units

Q. Using the distance formula, show that the given points are collinear.
$(1,-1),(5,2)$ and $(9,5)$.

Q.

Find the distance between the points (3, -6), (-2, 2)

Q. A square is formed by the points $(4,5),(12,5),(12,-3)$ and $(4,-3)$. Find the coordinates of the point at which the diagonals of the square intersect.

1. $(9,6)$
2. $(8,5)$
3. $(8,1)$
4. $(12,1)$

Q.

1. $25$
2. $\sqrt{45}$
3. $15$
4. $\sqrt{409}$

Q.

If the distance between points (p, –5), (2, 7) is 13 units, then $p$ is _____________

1. –3 or 7
2. –7 or 3
3. –3 or –7
4. 3 or 7

Q. If A and B are standing at (2, 7) and (9, -1) respectively, how far is A from B?

1. $\sqrt{93}$ units
2. $\sqrt{113}$ units
3. $\sqrt{73}$ units
4. $\sqrt{57}$ units