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## Introduction

In this article, we are going to discuss The Point Shortcut Tricks which contains the following contents such as co-ordinates axes, distance formula, section formula, types of centres like centroid, incentre, circumcentre, and orthocentre, etc.

In this The Point Shortcut Tricks, we will discuss Basic concepts, shortcut tricks, MCQ – Test series, and Explanations with shortcut tricks

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## Basic Concepts

Today, we are to discuss the following basic concepts such as distance formula, section formula, midpoint formula, centres like centroid, incentre, circumcentre, and orthocentre, etc.

**Rectangular Cartesian Co-ordinates**

Let XOX’ and YOY’ be two fixed straight lines, which intersect at right angles at ‘O’ (0, 0), then

- XOX’ and YOY’ are respectively known as the x-axis and y-axis.
- O(0, 0) is called origin.
- The ordered pair of real numbers (x, y) is called Cartesian coordinates of point P.
- The x – co-ordinate is called abscissa which is the distance of the point from the y-axis parallel to the x-axis.
- The y – coordinate is called ordinate which is the distance of the point from the x-axis parallel to the y-axis.
- x – coordinate of a point on the y-axis is zero.
- Y – co-ordinate of a point on the x-axis is zero.

**Quadrants**

The co-ordinate axes divide a plane into the four parts which are known as **quadrants.**

As the region of the areas XOY, X’OY, X’OY’and XOY’ are called first, second, third, and fourth quadrants respectively.

**Polar Co-ordinates**

The polar coordinates of the point are specified as (r, ϴ) Where r = distance of the point from the origin (radius vector) and ϴ = angle between the radius vector and x-axis which is known as a Vectorial angle.

**Relationship between Cartesian and polar Co-ordinates**

If (x, y) be the Cartesian coordinates of a point P lying in a plane and (r, ϴ) be its polar coordinates with respect to origin ‘O’ as the pole and x-axis as the initial line, then

To know about relationship cartesian coordinates and polar coordinates and more about Basic concepts of The Point click on the below link

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## Shortcut Tricks

In this article, we will also discuss the shortcut tricks related to all the above concepts.

**Shortcut Trick** To identify the right-angled triangle from the given three vertices of type A(a, b), B(a, c), and C(d, b) of an ABC

Here we observed that

x co-ordinates of vertex A = x co-ordinates of vertex B

y co-ordinates of vertex A = y co-ordinates of vertex C

In such a condition given triangle must be a right-angled triangle and right-angled at the vertex A(a, b)

To Buy this The Point Shortcut Tricks written by highly experienced Author Nitin Sharma click on the below link

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## MCQ – Test Series

Here we have the MCQ test series about The Point Shortcut Tricks look at below

Q.1 The mid points of sides of a triangle are (2, 4), (4, 6) and (6, 10). Then the co-ordinates of its vertices are

- (5, 8), (0, 2), (8, 12)
- (4, 8), (0, 0), (8, 12)
- (6, 8), (0, 0), (8, 10)
- None of these

Q.2 Number of integral interior points of the triangle having vertices (0, 0), (0, 31), and (31, 0) is

- 535
- 635
- 435
- 735

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## Explanations

Now we are to discuss the explanations of the point shortcut tricks of above questions

**Solution.1 **

The midpoints of sides of a triangle are P(2, 4), Q(4, 6), and R(6, 10). Then the coordinates of its vertices are A(4, 8), B(0, 0), C(8, 12). See below shortcut trick

In a ABC ,if P, Q, R are the midpoints of sides of triangle, then its vertices A, B, C are given by

A = P + R – Q B = P + Q – R C = R + Q – P

*solution.2*

Number of integral interior points of the triangle having vertices (0, 0), (0,31) and (31, 0) is given by = (31- 1)/2 x (31-2) = 15 x 29 = 435

To know more questions and explanations about The Point Shortcut Tricks click on the below link

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## conclusion

Finally, we say on behalf of the above discussion that The Point Shortcut Tricks article is very most important for us

So to but The Point Shortcut Tricks click on below link

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