Applications of Distance Formula

Q. $\text{In figure, ‘S’ is any point on the side}QR\text{of}△PQR.$
Prove that $PQ+QR+RP>2PS.$

Q.

Find the points on the $x$-axis which are at a distance of $2\sqrt{5}$ from the point $(7,-4)$. How many such points are there $?$

Q.

The lines x = -3 and y = -4 intersect at the point ___.

Q.

What is the distance of the point P (7, -6) from the x-axis and y-axis respectively? (Don't use Distance formula to find your answer)

1. 7 units from the x-axis and 6 units from the y-axis.

2. 6 units from the x-axis and 7 units from the y-axis.

3. 6 units from the x-axis and 6 units from the y-axis.

4. 7 units from the x-axis and 7 units from the y-axis.

Q.

The vertices of a triangle are $A(0,0),B(0,2)$and $C(2,0),$ then find the distance between its orthocenter and circumcenter

1. $0$

2. $\sqrt{2}$

3. $\frac{1}{\sqrt{2}}$

4. None of these

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.

Find the coordinates of the circumcenter of a triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). What is the circumradius of this triangle?

1. (5, 2) and 5

2. (5, 2) and 7

3. (5, 1) and 7

4. (5, 1) and 5

Q.

Can the following points form a triangle?
A(5, 5), B(4, 4) and C(3, 3)
If yes, which triangle it could be?

1. Right angled

2. Isosceles

3. Scalene

4. The three points don’t form a triangle.

Q.

For a triangle ABC, the true statement is –

1. = +

2. AC > AB + BC

3. AC < AB + BC

4. AC = AB + BC

Q.

In triangle ABC prove AB+BC+CA >2AB

Q. A point lies on positive direction of x-axis at a distance of 7 units from the y-axis. What are its Coordinates, if this lies in the negative direction of y-axis at a distance of 7 units from x-axis?

Q.

In triangle ABC, E and F are the mid points of the sides AC and AB respectively. The altitude AP to BC intersects EF at Q. Then

1. 

2. 

3. 

4. 

Q.

The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is

1. Isoscles

2. Equilateral

3. Scalene

4. None of these

Q. Write the answer of each of the following questions:
$\left(i\right)$ What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
$\left(ii\right)$ What is the name of each part of the plane formed by these two lines?
$\left(iii\right)$ Write the name of the point where these two lines intersect.

Q. The line x + 3 = 0 and y-4 = 0 meet at the point ______.

1. (3, -4)
2. (-3, 4)
3. (3, 4)
4. (3, -4)

Q.

A question was asked in a class
"The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?".
Unfortunately, no student could get it right.
What triangle would the three points form?

1. Isosceles

2. Scalene

3. Right angled

4. The three points don’t form a triangle

Q. Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius 20 m drawn in a park. Ishita throws a ball to Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is 24 m each, what is the distance between Ishita and Nisha.

Q.

In a triangle ABC this statement will always be true.

1. AB<BC<AC

2. AB+BC=AC

3. AB+BC<AC

4. AB+BC>AC

Q.

The point on x-axis equidistant from (5, 4) and (–2, 3) is ____ .

1. (3, 0)

2. (2, 0)

3. (4, 0)

4. (0, 2)

Q.

The co-ordinates of the vertices of Triangle ABC are $A(4,1),B(–3,2)$ and $C(0,k)$. Given that the area of $△ABC$ is 12 sq. units. Find the value(s) of $k$.

1. 5 only

2. only

3. 5 and

4. 4

Q. What is the ordinate of the point (6, 5)?

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

Q.

$x-y=0$ is a line which is ______________.

1. passing through (1, -1)

2. passing through origin

3. parallel to y-axis

4. parallel to x-axis

Q. A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the point B if AB and BC are parallel to the coordinate axes.

1. (2, 1)
2. (3, 2)
3. (1, 1)
4. (5, 4)

Q.

How do you find the distance between the points $\left(3,7\right)$, $\left(-2,-5\right)$?

Q.

The distance between A (2, 4) and B (3, 8) is :

1. $\sqrt{15}$ units

2. $\sqrt{17}$ units

3. 4 units

4. 4.5 units

Q. The distance between the points (4, 8) and (k, -2) is 10 units. Find the value of k.

Q.

If A(2, -3), B(3, 2), C(1, -2) and D(5, -4) are four points, then AB = CD.

1. True

2. False

Q. The line x + 3 = 0 and y-4 = 0 meet at the point ______.

1. (3, -4)
2. (-3, 4)
3. (3, 4)
4. (3, -4)

Q.

Find the point on the y-axis which is equidistant from A (3, - 4) and B (- 5, 9).

1. $(0,\frac{81}{28})$

2. $(0,3)$

3. $(0,\frac{81}{26})$

4. $(0,\frac{105}{26})$

Q.

For what value of $\frac{P}{Q}$ does A (a, a), B (-a, -a) and C (Pa, Qa) form the vertices of an equilateral triangle?

1. 1

2. -1

3. 2

4. -2