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Reflection of a Point About a Line and Divisibility Rules

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A Brief Explanation of Reflection of a Point About a Line

Do you find it easy to understand what a point means in mathematics? If not, then it's ok as this article discusses the point and the reflection of a point about a line in detail. A line is a figure formed when two points are connected with minimum distance between them, and both the ends extended to infinity. The reflection of a point about a line shows the mirror image of the original point. Reflection of a point about a line is a geometric concept that can be used to find any point on an intersecting line. It is important to understand this concept in order to have a deeper understanding of the mathematics behind it. In this article, we will focus on some issues related to these, which will help us to understand it better.


What is the Reflection of a Point about a Line?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Preimage and image are terms used to refer to the same thing in this context.


A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.


Reflection of a Point about a Line


Reflection of a Point about a Line


What is the Divisibility Rule in Maths?

A divisibility rule is a kind of shortcut that helps us to identify if a given integer is divisible by a divisor by examining its digits, without performing the whole division process.


The divisibility rules are as follows:


Divisibility by Number

Divisibility Rules

Divisible by 2

A number that is even or whose last digit is an even number, i.e. $0,2,4,6$ and 8.

Divisible by 3

The sum of all the digits of the number should be divisible by 3.

Divisible by 4

The number formed by the last two digits of the number should be divisible by 4 or should be 00.

Divisible by 5

Numbers having 0 or 5 as their ones place digit.

Divisible by 6

A number that is divisible by both 2 and 3.

Divisible by 7

Subtracting twice the number's last digit from the remaining digits gives a multiple of 7.

Divisible by 8

The number formed by the last three digits should be divisible by 8 or 000.

Divisible by 9

The sum of all the digits of the number should be divisible by 9.

Divisible by 10

Any number whose one's place digit is 0.

Divisible by 11

The difference between the sums of the alternative digits of a number is divisible by 11.

Divisible by 12

A number that is divisible by both 3 and 4.


Problems on Divisibility Rules

Here are some questions mainly related to divisibility rule, which are as follows;


Example- Verify that 28 may be divided by 2.

Ans: The rule states that if a number is even, it can be divided by two.

The number 28 is even. As a result, 28 is divisible by 2.


Example- Verify that 153 may be divided by 3.

Ans: The rule states that a number is divisible by 3 if the sum of its digits is a multiple of 3.

Sum of the digits in 153= 1+5+3 = 9

Nine is a multiple of three. As a result, 153 is divisible by three.


Example- Verify that 428 may be divided by 4.

Ans: The rule states that a number is divisible by 4 if its last two digits are zeros or if the sum of its last two digits is also a number that is divisible by 4.

The number generated by the last two digits of the number 428 is 28, which is divisible by 4.

As a result, 428 is divisible by 4.


Worksheet on Divisibility Rules

Here are some Worksheet questions mainly related to divisibility rule, which are as follows;


Q 1. Verify that 64 may be divided by 2

Ans. Yes


Q 2. Verify that 270 may be divided by 3

Ans. Yes


Q 3. Verify that 864 may be divided by 4

Ans. Yes


Q 4. Verify that 525 may be divided by 5

Ans. Yes


Q 5. Verify that 618 may be divided by 6

Ans. Yes


Summary

The reflection of a point about a line is the point that is exactly opposite to the first point on the line. In mathematics, reflection of a point about a line is often used as an introductory topic. The reflection of a point about a line can be defined as the point that is exactly opposite to the first point on the line. In this section, we explored the reflection of a point about a line.


First, we need to understand what a line is and what its properties are. A line has two endpoints and it is infinite in both directions. The endpoint at one end is called the starting point and the endpoint at the other end is called the ending point. Apart from this, in this article, we have also discussed Divisibility Problems and related concepts, which helps to understand this article better.

Last updated date: 02nd Oct 2023
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FAQs on Reflection of a Point About a Line and Divisibility Rules

1. What is the use of divisibility rules?

In math, divisibility tests are important to learn as it helps us to ease out our calculations where we have to do multiplication and division. We can quickly identify whether a particular number is divisible by another number or not by applying divisibility rules.

2. What will happen if the reflection of the point is over the Y-axis?

When a point is reflected across the Y-axis, the Y-coordinates remain the same. But the X-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across the Y-axis is (-x, y).

3. What will happen if the reflection of a point is over the x-axis?

When a point is reflected across the X-axis, the x-coordinates remain the same. But the Y-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across X-axis is (x, -y).