Straight Lines ...

Let $$ABCD$$ be  a square of a side length $$1$$. Let $$P,Q,R,S$$ be points in the interiors of the sides $$AD,BC,AB,CD$$ respectively, such that $$PQ$$ and $$RS$$ intersect at right angles. If $$PQ=\cfrac { 3\sqrt { 3 }  }{ 4 } $$ then $$RS$$ equals

A frog is presently located at the origin $$\left( 0,0 \right)$$ in the $$xy$$-plane. It always jumps from a point with integer coordinates to a point with integer coordinates moving a distance of $$5$$ units in each jump. What is the minimum number of jumps required for the frog to go from $$\left( 0,0 \right)$$ to $$\left( 0,1 \right) $$?

Find the area (in square units) of the triangle whose vertices are $$(a, b+c), (a, b-c) $$ and $$(-a, c). $$

The angle between the lines $$ 2x+11y-7=0$$
and $$ x+3y+5=0$$ is equal to :

The slope of a straight line passing through A( -2, 3) is  -4/3. The points on the line that are 10 units  away from A are 

If D (3, -1), E (2, 6) and F (5, 7) are the vettices of the sides of $$\Delta DEF$$, the area of triangle DEF is sq. units. 

Let $$P$$ be $$(5, 3)$$ and a point $$R$$ on $$y = x$$ and $$Q$$ on the x-axis be such that $$PQ + QR + RP$$ is minimum. Then the coordinates of $$Q$$ are

The points $$(-1,0)$$ and $$(-2,1)$$ are the two extremities of a diagonal of a parallelogram. If $$(-6,5)$$ is the third vertex, then the fourth vertex of the parallelogram is

The point on the line $$4x+3y=5$$, which is equidistant from $$\left( 1,2 \right)$$ and $$\left( 3,4 \right) $$, is

$$A=(4, 2)$$ and $$B=(2, 4)$$ are two given points and a point $$P$$ on the line $$3x + 2y + 10 = 0 $$ is given then. which of the following is true.