Greetings
I am Muhammad Ahmad from Pakistan
Welcome to my post, my dear friends. How's everything going? I hope that you all will be fine and enjoying your life. I am also fine and good. Alhumdullilah
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Today I am going to participate in the SLC contest organized by Dear. @sergeyk, In this I have to learn about Geometry and tell that practically.I have also a lot of experience in Geometry as I am a student of 10th Standard and I have learn a lot of Geometry in my school.But here it would be little challenging because I have to do geometry practically on a website known as GeoGebra, so now without wasting any kind of time lets get into it.For participating in this, I have to answer few questions.So lets begin.
Tell about the number line and the coordinate plane. When did you first learn about coordinates? Was it difficult? |
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I learnt it first at my school more specifically in 9th Standard, in which I learned that A Number line is a straight line.Some of the numbers are being written on this Straigh line,In the centre of that line their would be a point of ZERO.The numbers which are written on the right side of the line would be positive as it would be increase like ( +1, +2, +3. +4, +5 ) and the numbers that are written on the left side would be negative as it would be decrease like ( -1, -2, -3, -4, -5 )
Line Segment
Now I would tell you about the coordinate plate.So basically a coordinate plane consists of two lines.One is Horizontal line and the other is vertical line.They both are perpendicular.The horizontal line is known as X-Axis and the vertical line is known as Y-Axis.Both of this lines interest each other to one which which is the point of origin.In coordinate plane their are four quadrants.First, second, third and fourth quadrant.
I learnt about coordinates the last year in 9th Standard from Forward Public School Peshawar, Pakistan.One of my honorable madam teach us about the cordinates but at first I did not get it.Then when the paper came then I told my tuition tutor that could you kindly tell me about this coordinates as I cant understand from my Madam at school.Then when I learnt it from my tutor in the tuition then I get a little control over it.But with practice I tool full control over it and now I understand it very greatly.Also in this subject I got 71 out of 75 marks which proves that I leant it very well.
Connect the pairs of points with vectors. Which vectors are formed? Show these vectors on the plane. A(-3, 11), B(4,7), C(0,4), D(4,0), E(-4,-7), F(11,3). |
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- In this task we have to each vector with the given points and the given points are mentioned below:
| A (-3,11) |
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| B (4,7) |
| C (0,4) |
| D (4,0)) |
| E (-4,-7) |
| F (11,3) |
The method I would use is the Subtraction method and here I will display one few as told to us by our instructor.So now I am displaying the last 2 ones by subtraction method.
AF Vector:
AF = (11-(- 3),3-11)
AF = (11+3,-8)
AF = (14,-8)
- AE Vector:
AE = (-4 - (-3),-7-11)
AE = (-4+3,-18)
AE = (-1.-18)
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Place the vectors a(3,7), b(-1,-3), and c(1,5) on the plane.Construct the vector a + b + c. |
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- In this task we have some given date which is Vector a = (3,7), Vector b = (-1,-3), Vector c = (1,5). First of all now we have to place it wisely on the coordinate plate.For this we have to take the start from the origin point which is (0,0) and we have to draw vector a from the origin point to the (3,7) and now we have to draw vector b from the end point of vector b from (3,7) to the (3+(−1),7 + (−3)) = (2,4) and after that we have to draw vector c which will be starting from the end point of vector b which is (2,4) to the (2+1,4+5) = (3,9).
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- Now we have to add up these three vectors.
(3,7) + (−1,−3) + (1,5) = (3−1+1,7−3+5) = (3,9)
So the total vector from point (0,0) to the final point is (3,9).
Place two random points and determine their coordinates.Create a vector from these points and write its coordinates. |
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So here in this task, first of all we have to take 2 random points.So for this I have taken R (2, 5) and S (6, 8).Now we get the two points and now we have to find two vectors RS, so we would find it with a formula and the formula is given below:
Formula: RS = (x2−x1, y2-y1)
Now putting values in this formula, we get
RS = (6−2,8−5) = (4,3)Now we have to double the vector and for this we have to simply multiply 2 with the upper equation.So lets begin.
2×RS = (2×4, 2×3) = (8,6)
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Construct three arbitrary vectors: a, b, k.Build the vectors u = a + b and v = b - k. |
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- So now we have to do the last task and for this some of the vectors are given.The vectors that are given to us are A = (2,3), B = (-1,4), K = (3,-2).Now with the help of these vectors we have to draw an arbitrary vector.So without wasting any time lets get into it.
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A = (2,3), B = (-1,4), K = (3,-2)
First of all we have to calculate u = a + b so by adding the vectors we get,
u = a+b = (3,2) + (−1,4) = (3−1,2+4) = (2,6). After that we have to calculate v = b-k so now put values into it. we get, v = b−k = (−1,4) − (2,−3) = (−1−2,4−(−3)) = (−3,7).Now we have to calculate u + v and for finding this we have to put values into it, so lets begin. u+v = (2,6) + (−3,7) = (2−3,6+7) = (−1,13). Now calculate the last one which is:
u - v, u−v=(2,6) − (−3,7) = (2+3, 6−7) = (5,−1).u = (2,6)
v = (-3,7)
u + v = (-1,13)
u - v = (5,-1)
Bonus Task : |
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The projection of vector shows that how much the first vector points in the direction of the second vector.We can understand it by its mathematical form too.The mathematical form of Vector Projection is:
