Area of Triangle Using Coordinates

Q.

If the coordinates of two points A and B are (3, 4) and (5, -2) respectively. Then, the coordinates of any point P, if PA = PB and area of $\Delta$ PAB = 10, are

1. (7, 5), (1, 0)

2. (2, 7), (1, 0)

3. (7, 2), (1, 0)

4. (7, 2), (- 1, 0)

Q.

The area of the triangle formed by the line $x+3y=12$ and the coordinate axes is:

1. $12sq.units$

2. $18sq.units$

3. $24sq.units$

4. $30sq.units$

Q.

The points (3, 3), (h, 0) and (0, k) are collinear if

1. 

2. 

3. 

4. 

Q. $A=(2,3,0)$ and $B=(2,1,2)$ are two points. If the points P, Q are on the line AB such that AP$=$PQ$=$QB then PQ$=?$

1. $\sqrt{2}$
2. $2\sqrt{2}$
3. $6\sqrt{2}$
4. $\sqrt{8/9}$

Q. If $(-4,0)$ and $(1,-1)$ are two vertices of a triangle of area $4$ sq. units, then its third vertex lies on

1. $y=x$
2. $5x+y+12=0$
3. $x+5y-4=0$
4. $x+5y+12=0$

Q. In a triangle $ABC$, $A=(\alpha ,\beta ),B=(2,3),C=(1,3)$ and point $A$ lies on line $y=2x+3$ where $\alpha ,\beta \in I$. Area of triangle $△ABC$, $\Delta$ is such that $\left[\Delta \right]=5$. Possible coordinates of $A$ are (where $[.]$ represents greatest integer function)

1. $(2,3)$
2. $(5,13)$
3. $(-5,-7)$
4. $(-3,-5)$

Q. Given a triangle whose vertices are at $(0,0),(4,4)$ and $(10,0)$. A square is drawn in it such that its base is on the x - axis and its two corners are on the 2 sides of the triangle. The area of square is equal to

1. $\frac{400}{49}$
2. $\frac{400}{25}$
3. $\frac{625}{16}$
4. $\frac{625}{49}$

Q.

What is the area of $\text{∆ABC}$ with vertices $A(2,3),B(1,-3),$and $C(-3,1)$?

Q. The vertices of a triangle $OBC$ are $O(0,0),B(-3,-1),C(-1,-3)$, then the equation of the line parallel to the side $BC$ and cutting the sides $OB$ and $OC$ and at a distance $\frac{1}{2}$ from the origin is

1. $x+y-\frac{1}{2}=0$
2. $x+y-\frac{1}{\sqrt{2}}=0$
3. $x+y+\frac{1}{2}=0$
4. $x+y+\frac{1}{\sqrt{2}}=0$

Q.

If the area of the triangle formed by the lines $y=x$, $x+y=2$ and the line through $P(h,k)$ and parallel to $x$-axis is $4h^2$, the locus of $P$ can be

1. $2x-y+1=0$

2. $2x+y-1=0$

3. $x-2y+1=0$

4. $x+2y-1=0$