Properties of Distance

Q. One side of a rectangle lose along the line 4x + 7y + 5 = 0. Two of its opposites vertices are ( -3, 1) and (1, 1). Find the equations of the lines containing other three sides.

Q.

Which of the given points lie on the line x - y = 5?

1. (4, -1)

2. All of the above

3. (7, 2)

4. (3, -2)

Q. 1.find the equation of the line passing through the point(2, 3) and making intercept of lengh 2 units between the lines Y+2X=3 and Y+2X =5. 2.Let (x, y, z) be points with integer co-ordinates satisfying the system of homogeneous equations 3x-y-z=0, -3x+z=0, -3x+ 2y +z=0.The no of such points for which x2(square) + y2(square)+z2(square) is less than or equal to100.

Q. If (3, x) is the mid-point of the line segment joining the points A(8, −5 ) and B(−2, 11), then find the value of ‘x ’

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

Q.

(0, 4) (1, 2) (2, 0) (3, -2) are all on the line 2x + y = 4

1. True

2. False

Q.

For a line whose equation is 2x + y = 5, which one of the following points lies on it ?

1. (-2, 1)

2. (2, 1)

3. (3, 2)

4. (1, 2)

Q.

The coordinates given below lie on 2x - y + 4 = 0

$$\begin{array}{ccccc}x& 1& 2& 4& -2\\ y& 6& 8& 10& 0\end{array}$$

1. True

2. False

Q.

The value of ‘k’ for which the points (1, 2), (5, 6) and (k, 1) are collinear is

1. 0

2. 1

3. 2

4. 3

5. 3

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.

Which of these lines pass through the point (2, -2)?

1. x + y = 0

2. 3x + 4y + 2 = 0

3. x - 5y = 12

4. All of the above

Q. Find the equation to the straight line parallel to 3x − 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, −1).

Q. If the given points lie on the straight line, then they are said to be

1. Collinear
2. non-collinear
3. Incentre
4. Centroid