Maths

A point P (a, b) is reflected in the x-axis to P’ (2, -3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.

A point \[P\text{ }\left( a,\text{ }b \right)\] is reflected in the \[x-hub\] to \[P'\text{ }\left( 2,\text{ }-\text{ }3 \right).\] We realize that, \[{{M}_{x}}~\left( x,\text{ }y \right)\text{...

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The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6). (i) State the name of the mirror line and write its equation. (ii) State the co-ordinates of the image of (-8, -5) in the mirror line.

(I) We realize that, impression of a point \[\left( x,\text{ }y \right)\]in \[y-hub\] is \[\left( -\text{ }x,\text{ }y \right).\] Thus, the point \[\left( -\text{ }2,\text{ }0 \right)\] when...

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Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1; points (0, -3) and (0, 1) are invariant points on reflection in line L2. (i)Write down the images of P and Q on reflection in L2. Name the images as P” and Q” respectively. (ii) State or describe a single transformation that maps P’ onto P”.

(i) \[P\text{ }=\text{ }Image\text{ }of\text{ }P\text{ }\left( 3,\text{ }4 \right)\text{ }in\text{ }{{L}_{2}}~=\text{ }\left( -3,\text{ }4 \right)\] Also, \[Q\text{ }=\text{ }Image\text{ }of\text{...

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Points (3, 0) and (-1, 0) are invariant points under reflection in the line L1; points (0, -3) and (0, 1) are invariant points on reflection in line L2. (i) Name or write equations for the lines L1 and L2. (ii) Write down the images of the points P (3, 4) and Q (-5, -2) on reflection in line L1. Name the images as P’ and Q’ respectively.

(I) We realize that, each point in a line is invariant under the appearance in a similar line. As the focuses \[\left( 3,\text{ }0 \right)\]and \[\left( -\text{ }1,\text{ }0 \right)\]lie on the...

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In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: (i) βˆ†APC and βˆ†BPD are similar. (ii) If BD = 2.4 cm, AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and PC.

Answer: (I) In \[\vartriangle \mathbf{APC}\text{ }\mathbf{and}\text{ }\vartriangle \mathbf{BPD}\]we have \[\angle APC\text{ }=\angle BPD\] [Vertically inverse angles] \[\angle ACP\text{ }=\angle...

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Asharaf went to see a movie. He wanted to purchase a movie ticket for Rs. 80. As the ticket for Rs. 80 was not available, he purchased a ticket for Rs. 120 of upper class. How much extra GST did he pay for the ticket? (GST for a ticket below Rs. 100 is 18% and GST for a ticket above Rs. 100 is 28%)

From the inquiry, we have GST on ticket of \[Rs.\text{ }80\text{ }=\text{ }18percent\text{ }of\text{ }80\] \[=\text{ }18/100\text{ }x\text{ }80\text{ }=\text{ }Rs.\text{ }14.40\] GST on ticket of...

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Mr. Malik went on a tour to Goa. He took a room in a hotel for two days at the rate of Rs. 5000 per day. On the same day, his friend John also joined him. Hotel provided an extra bed charging Rs. 1000 per day for the bed. How much GST, at the rate of 28% is charged by the hotel in the bill to Mr. Malik for both the days?

From the inquiry, we have The amount of bill \[=\text{ }cost\text{ }of\text{ }hotel\text{ }room\text{ }x\text{ }no.\text{ }of\text{ }days\text{ }+\text{ }additional\text{ }bed\text{ }charges\text{...

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For the following transaction from Delhi to Jaipur, fill in the blanks to find the amount of bill: MRP = Rs 50,000, Discount % = 20%, GST = 28% Discount = Selling price (discounted value) = CGST = SGST = IGST = Amount of Bill =

Given, MRP \[=\text{ }Rs\text{ }50,000\] Discount % \[=\text{ }20percent\] GST $=28percent$ Presently, \[Discount\text{ }=\text{ }20percent\text{ }of\text{ }50,000\text{ }\] \[=\text{ }\left( 20/100...

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For the following transaction within Delhi, fill in the blanks to find the amount of bill: MRP = Rs 12,000, Discount % = 30%, GST = 18% Discount = Selling price (discounted value) = CGST = SGST = IGST = Amount of Bill =

Given, MRP =Β Rs 12,000 Discount = 30% GST = 18% Presently, \[Discount\text{ }=\text{ }30%\text{ }of\text{ }12,000\] \[=\text{ }\left( 30/100 \right)\text{ }x\text{ }1200\text{ }=\text{ }Rs\text{...

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