Analytic geometry Quiz 1

Question 1

Which of the following conditions will be true if the distance between the points $$\left( 3q,2p \right)$$ and $$\left( p,-q \right)$$ is given by$$\sqrt{{{p}^{2}}+12{{q}^{2}}-2pq}$$?

Accepted Answer

$$2{{p}^{2}}={{q}^{2}}$$

Answer

$${{p}^{2}}={{q}^{2}}$$

Answer

$${{p}^{2}}=3{{q}^{2}}$$

Answer

$${{p}^{2}}=3q$$

Question 2

What is the value of $$a	ext{ and }b$$, if $$\left( \dfrac{1}{6},5 ight)$$ is a mid-point of a line joining points $$\left( \dfrac{a}{6},5a ight)	ext{ and }\left( \dfrac{-b}{8},3b ight)$$?

Accepted Answer

$$a=2,b=0$$

Answer

$$a=-1,b=-3$$

Answer

$$a=-1,b=1$$

Answer

$$a=3,b=1$$

Question 3

Find the equation of a line whose y-intercept is $$\dfrac{7}{3}$$ and parallel to another line such that the sum of their slopes is $$\dfrac{5}{3}$$.

Accepted Answer

$$5x-6y+14=0$$

Answer

$$5x-5y+3=0$$

Answer

$$6x+6y+14=0$$

Answer

$$7x+4y+4=0$$

Question 4

If $$	ext{R}\left( -4,\dfrac{x}{3} ight),	ext{S}\left( 6,\dfrac{-1}{2} ight)	ext{ and T}\left( 12,\dfrac{x}{2} ight)$$ are the three vertices of a $$\Delta 	ext{RST}$$ whose area is given as 25 sq. units, then find the value of $$x$$.

Accepted Answer

$$3$$

Answer

4

Answer

6

Answer

$$\dfrac{10}{3}$$

Question 5

If $$	ext{A}(5,-1),	ext{B}(2,3)	ext{ and C}$$ are the three vertices of a $$\Delta 	ext{ABC}$$ where $$\angle 	ext{A}={{60}^{{}^\circ }}$$ and $$	ext{AC}=4cm$$, then find the length of BC.

Accepted Answer

$$\sqrt{21}cm$$

Answer

$$\sqrt{23}cm$$

Answer

$$4\sqrt{2}cm$$

Answer

$$5cm$$