What is distance formula and its use

The distance formula is a mathematical formula used to calculate the distance between two points in a plane. The formula is: d = √((x2 - x1)² + (y2 - y1)²)Where d is the distance between the two points, (x1, y1) and (x2, y2) are the coordinates of the two points.It is used in a wide range of fields such as physics, engineering, computer graphics, and game development to measure the distance between objects or points in a 2D or 3D space. It can also be used in statistics, economics and other fields where the distance between observations is important.

What is section formula and its use

The section formula, also known as the midpoint formula, is a mathematical formula used to find the coordinates of a point that divides a line segment into two equal parts. The formula is:M = ((x1 + x2)/2 , (y1 + y2)/2)Where M is the midpoint of the line segment, (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.The section formula can be used to find the midpoint of a line segment in a coordinate plane, which is useful in applications such as computer graphics, game development, and engineering. The midpoint formula is also used in statistics and economics to find the average value of a set of observations.It can also be used to find the coordinates of any point that divides a line segment into two parts in a ratio of m:n where m and n are integers.It is known as section formula because it can be used to find a point of a line segment that is dividing it in a specific ratio (m:n).

What is section formula when it divides externally and internally

The section formula can also be used to find the coordinates of a point that divides a line segment into two parts externally or internally.

When a line segment is divided externally, the point of division is outside the line segment. In this case, the coordinates of the point of division can be found using the following formula:P = ( (mx2 - nx1)/(m-n) , (my2 - ny1)/(m- n) )Where P is the point of division, (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and m and n are the external division ratios.

When a line segment is divided internally, the point of division is inside the line segment. In this case, the coordinates of the point of division can be found using the following formula:P = ( (mx1 + nx2)/(m+n) , (my1 + ny2)/(m+n) )Where P is the point of division, (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and m and n are the internal division ratios.These section formula are very useful in geometry, engineering, physics and other fields to find the coordinates of a specific point in a line segment, for example to find the point of tangency in a circle, or to find the point of intersection between two lines.

What is formula for Area of triangle

The coordinates formula: Area = (1/2) | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | Where (x1,y1), (x2,y2), (x3,y3) are the coordinates of the three vertices of the triangle.
It's important to note that all the above formulas are for calculating area of a triangle in 2D plane, for 3D space the formulas would be different.All of these formulas are used in geometry, engineering, physics, and other fields to calculate the area of a triangle and make geometric calculations.

How we find three points are collinear using coordinate geometry

In coordinate geometry, three points (x1, y1), (x2, y2), and (x3, y3) are collinear if they lie on the same straight line. One way to check if three points are collinear is to use the slope formula and check if the slope between each pair of points is the same.The slope formula is: m = (y2 - y1) / (x2 - x1)So, to check if three points are collinear, you can use the slope formula to find the slope between point 1 and point 2, point 2 and point 3, and point 1 and point 3. If the slopes are equal, the points are collinear.Another way to check if three points are collinear is to use the area of the triangle formula using these three points as vertices. If the area of the triangle is zero, then the three points are collinear.Area = (1/2) | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |If the above area is zero, then the three points are collinear.Both of these methods are equivalent and can be used to check if three points are collinear

Mock Test Series

Que 1
The coordinates of the origin
a) (0,1)
b) (1,0)
c) (0,0)
d) (1,2)

Ans (c)

Que 2
The points (-5,2)and (2,-5) lie in the
d) on y axis

Ans ( c)

Que 3
Point (0,7) lies
a) x axis
b) y axis

Ans (b)

Que 4
Point (7,0) lies
a) x axis
b) y axis

Ans (a)

Que 5
The point at which the two co-ordinate axes meet is called
a) abscissa
b) ordinate
c) origin

Ans (c)

Que 6
The perpendicular distance of the point P (3,4) from the y-axis
a) 3
b) 4
c). 5
d) 7

Ans (a)

Que 7
A point both of whose coordinate are negative will lie in the

Ans (c)

Que 8
Points (1,-1),(-2,-2)(-3,3),(2,4) lie

Ans (d)

Que 9
The points whose abscissa and ordinate have different sign will lie in

Ans ( d)

Que 10
If the coordinates of the two points P (-2,3) and Q ( -3,5) then abscissa of P -abscissa of Q is

a) -5
b) 1
c) -1
d) -2

Ans (b)

Sonika Agarwal