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Hey there, everyone!
How is it going today? How’s the optimism? Hope it’s there. As long as you believe, that everything will be fine, there will always be something to look forward to.
Alright, so today, we won’t dwell in nostalgia because present, after all, is the reality. Could be harsh, could be not.
Now, I want to begin with talking a bit about something I have really liked a lot since always (Okay yeah, maybe I am getting a tad bit nostalgic, after all).
Those beautiful and heavily dense meshy green lines, running parallelly at a millimeter gap from each other, both vertically and horizontally. Such a satisfying use of paper. I have found co-ordinate geometry to be pretty fascinating.
But today, I will keep this blog kind of short and just try to tell you just how simple and sensible the Cartesian Plane is. Give it sometime and you’ll understand why exactly I used ‘sensible’.
First, here are a few basic geometry and co-ordinate geometry questions, you need to solve.
1.There is a right-angled triangle ABC, right angled at B. Length AB is 4 cm and AC is 5cm. What is length BC?
2.There is a rectangle PQRS with sides of length PQ = 10 cm and QR = 2 cm. What is the area of the rectangle.
3. What is the radius of a circle with area 154 cm sq. Use π = 22/7
4.There is a circle with centre O and diameter AB. A line each from A and B is drawn and they meet on the circumference at point P. Now, AP is 12 cm, and BP is 16, what is the length of the radius of the circle?
5.x + y = 20; 3x + 3y = 60. How many points do these lines have in common?
Now, after having solved these 5 questions, I need you to take out your graph papers. (You’ll need quite a few of those). Grab your scales, pencils and erasers and start.
Starting from the first question, try solving each question, by drawing the quadrilaterals and equations on the graph paper. Try obtaining absolute or approximate answers and compare them with the first time.
Do send in your observations at firstname.lastname@example.org
Now check out these next few questions.
1.Plot, (0,0), (0,20) and (20,0). Calculate the area of the figure enclosed by joining these three points.
2.Imagine you’re at (0,0). Now you go 10 centimeter steps to the East. Then go 2 centimeter steps to the North. Now walk back to the point where you started from, taking the shortest path possible. What is the area enclosed by all the paths you took?
3.There is a donkey tied to a pole, with a rope of length 7 units. The pole is placed at the point (2,1).
a.What do you think is the motion of the donkey? As in, what kind of shape does one complete movement of the donkey, form?
b.If the donkey takes 6 minutes to complete one full motion, what is distance it covers, in 3 minutes?
c.If it starts from (9,1), what will be it’s co-ordinates at 3 minutes from the start and at 6 minutes from the start?
4.Locate the co-ordinates (0,12) and (16,0). Join the points. Fix your compass at the centre of the line so drawn and draw a circle taking the distance of the point from either of the axes along the line, as radius.
Which of the following is true about the circle so formed?
a.The radius of the circle is 12 cm.
b.The circle passes through (0,0).
c.The circle passes through (12,16).
I would totally advise you get hold of 10 plus graph papers and do all the nine questions on the papers. Especially the last four. Then compare them to your previously obtained results and I hope you are surprised at some of the observations you make.
Because, if you are, then you did a good job. And if you aren’t then either, you already saw through it all or you didn’t see through any of it.
With this, I will take your leave this time. Do send in the solutions and observations, to the aforementioned mail id.
Thank you so much for reading and solving the questions. Hope you had as much fun solving them as much I had making the questions for you.
These questions would help you see, hoe elegant and truthful co-ordinate geometry actually is. You can vividly see, it all happening in front of you.
Alright then. Till next time! Stay hopeful!
All the best!
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