Distance between Two Points on the Same Coordinate Axes

Q.

Check whether $(5,-2)$, $(6,4)$ and $(7,-2)$ are the vertices of an isosceles triangle.

Q.

If $y=mx$ be one of the bisectors of the angle between the lines $a{x}^2-2hxy+b{y}^2=0$, then

1. $h\left(1+m^2\right)+m\left(a-b\right)=0$

2. $h\left(1-m^2\right)+m\left(a+b\right)=0$

3. $h\left(1-m^2\right)+m\left(a-b\right)=0$

4. $h\left(1+m^2\right)+m\left(a+b\right)=0$

Q.

What is the equation of the bisectors of the angle between lines represented by equation $4x^2-16xy-7y^2=0$.

1. $8x^2+11xy-8y^2$

2. $8x^2-11xy-8y^2$

3. $16x^2+11xy-16y^2$

4. $16x^2+11xy+16y^2$

Q.

The diagonals of a parallelogram$PQRS$are along the lines$x+3y=4$ and $6x-2y=7$.Then$PQRS$ must be

1. Rectangle

2. Square

3. Cyclic quadrilateral

4. Rhombus

Q.

If the bisectors of the angles between the pairs of lines given by the equation $a{x}^2+2hxy+b{y}^2=0$ and $a{x}^2+2hxy+b{y}^2+\lambda \left(x^2+y^2\right)=0$ be coincident, then $\lambda =$

1. $a$

2. $b$

3. $h$

4. Any real number

Q.

If the pairs of lines $x^2-2nxy-y^2=0$ and $x^2-2mxy-y^2=0$ are such that one of them represents the bisectors of the angles between the other, then

1. $mn=1$

2. $m+n=mn$

3. $mn=-1$

4. $m-n=mn$

Q. If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are

(a) (0, 3)

(b) (3, 0)

(c) (0, 0)

(d) (0, −3)

Q.

What is the equation of the bisectors of the angle between the lines represented by the equation $x^2-y^2=0$?

1. $x=0$

2. $y=0$

3. $xy=0$

4. None of these

Q.

Name The Type Of Quadrilateral Formed By The Following Points -$(-3,5),(3,1),(0,3),(-1,-4)$ And Give Reasons For Your Answer

Q.

The equation of the smallest circle passing through the points $(2,2)$ and $(3,3)$ is

1. $x^2+y^2+5x+5y+12=0$

2. $x^2+y^2-5x-5y+12=0$

3. $x^2+y^2+5x-5y+12=0$

4. $x^2+y^2-5x+5y-12=0$

Q.

The point on Y-axis equidistant from (–3, 4) and (7, 6) is ___.

1. (0, 15)

2. (0, 14)

3. (0, 13)

4. (15 , 0)

Q.

Question 1
Show that the points A(1, 2), B(-1, -16) and C(0, -7) lie on the graph of the linear equation:
y = 9x - 7.

Q.

Point P $\left(0,2\right)$ is the point of intersection of $y$-axis and perpendicular bisector of the line segment joining the points A $\left(-1,1\right)$ and B $\left(3,3\right)$. State whether the following statement is true or false. Justify your answer.

Q.

In figure, AB || DC. Find the value of x

Q. Question 5
From the choices given below, choose the equation whose graphs are given in Fig. $4.6$ and Fig. $4.7$.

$ForFig.4.6$ $ForFig.4.7$
$\left(i\right)y=x$ $\left(i\right)y=x+2$
$\left(ii\right)x+y=0$ $\left(ii\right)y=x-2$
$\left(iii\right)y=2x$ $\left(iii\right)y=-x+2$
$\left(iv\right)2+3y=7x$ $\left(iv\right)x+2y=6$

​​​​​​​

Q.

With the vertices of $△$ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

Q.

The $y$-coordinate of any point lying on the $x$-axis will be zero. State whether the statement is true (T) or false (F).

1. True
2. False

Q.

If the coordinates of the mid points of the sides of a triangle are (1, 1), (2, – 3) and (3, 4) Find its centroid.

Q. The distance of the point (4, 7) from the x-axis is

(a) 4

(b) 7

(c) 11

(d) $\sqrt{65}$

Q.

In the figure below, ABCD is a square. Find the coordinates of B, C, D.

Q. Question 84
Fill in the blanks to make the statements true.
​​​​​​​Diagonals of a rectangle are ___.

Q.

Find the lengths of the medians of a triangle ABC whose vertices are A(7, –3), B(5, 3) and C(3, –1). [4 MARKS]

Q.

The angle of depression of the front end of a ship as seen from the top of 120 m high light house is 60${}^{\circ }$. How far is the ship from the light house?

Q.

The distance between two points on a line parallel to Y-axis = ___

1. difference of their of x-coordinates
2. difference of their of y-coordinates
3. Zero
4. sum of their of x-coordinates

Q.

Find the values of x and y in the following rectangle.

Q.

The equation $xy-a^2=a(x+y)$ represents

1. A parabola

2. Two perpendicular lines

3. An ellipse

4. Twp parallel straight lines

Q.

Find the lengths of the medians of a triangle ABC whose vertices are A(7, –3), B(5, 3) and C(3, –1).

Q. Question 8
Find the values of y for which the distance between the points P (2, - 3) and Q (10, y) is 10 units.

Q.

The distance between two points on a line parallel to X-axis = ___

1. difference of their of x-coordinates
2. difference of their of y-coordinates
3. sum of their of x-coordinates
4. sum of their of y-coordinates

Q. The distance of the point (4, 7) from the y-axis is

(a) 4

(b) 7

(c) 11

(d) $\sqrt{65}$