Rotations Quiz 1

Question 1

An object is stuck in a canal given by the equation $${{x}^{2}}-{{y}^{2}}=10$$ . If the system $$($$The axes$$)$$ are rotated by the angle of $${{45}^{\circ}}$$ in clockwise direction, what will be the new equation of the object?

Accepted Answer

$$XY=5$$

Answer

$$XY=10$$

Answer

$$XY=25$$

Answer

Inadequate Information

Question 2

A circle is given by equation $${{x}^{2}}+{{y}^{2}}=4$$ . The axes are rotated such that they are expressed by the line $$x=y$$ and  $$x=-y$$ . Find the new equation of the circle

Accepted Answer

$${{X}^{2}}+{{Y}^{2}}=4$$

Answer

$${{X}^{2}}+{{Y}^{2}}=16$$

Answer

$${{X}^{2}}+{{Y}^{2}}=2$$

Answer

$$X+Y=4$$

Question 3

An equation is present such that$$3{{x}^{2}}+2xy+{{y}^{2}}=1$$. A student wants to rotate the axes themselves to simplify the equation and remove the xy term. By what angle must the axes be rotated?

Accepted Answer

$$	heta ={{67.5}^{\circ}}$$

Answer

$$	heta ={{22.5}^{\circ}}$$

Answer

$$	heta ={{45}^{\circ}}$$

Answer

$$	heta ={{135}^{\circ}}$$

Question 4

A point is mapped by a girl to be $$(17,35)$$. She rotates the point by $${{180}^{\circ}}$$ clockwise and then with the same angle counterclockwise for ‘N’ number of times. What are the final coordinates of the point?

Accepted Answer

Same as before

Answer

Lie on x axis

Answer

Lie on the y axis

Answer

Lie on the line $$x=y$$

Question 5

A child is playing with an analog clock, such that he moves the hour hand which was on the position mapped by $$(3,7)$$ in an anticlockwise sense by $${{270}^{\circ}}$$, thereby ruining the clock. Find the new coordinates to correct the clock.

Accepted Answer

(7,-3)

Answer

Insufficient information

Answer

(7,3)

Answer

(-7,-3)