Area of Triangle Using Coordinates

Q.

The line $3x+2y=24$ meets $y$-axis at $A$ and $x$-axis at $B$. The perpendicular bisector of $AB$ meets the line through $\left(0,-1\right)$ parallel to $x$-axis at $C$. The area of the triangle $ABC$ is

1. $182$ sq. units

2. $91$ sq. units

3. $48$ sq. units

4. None of these

Q. A line L passes through the points (1, 1) and (2, 0) and another line L’ passes through $[\frac{1}{2},0]$ and perpendicular to L. Then the area of the triangle formed by the lines L, L’ and y –axis, is

1. 
2. 
3. 
4. 

Q.

A square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinate axes. The

coordinates of its vertices are

1. (-6, -9), (-6, 5), (8, -9) and (8, 5)

2. (-6, 9), (-6, -5), (8, -9) and (8, 5)

3. (-6, -9), (-6, 5), (8, -9) and (8, -5)

4. (-6, -9), (-6, 5), (8, 9) and (8, 5)

Q.

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h, k) with the lines y=x and x+y=2 is $4h^2$. Find the locus of the point P.

1. y=2x+1

2. y=-2x+1

3. y-2x+1 = 0

4. 2y-x+1 = 0

Q.

Without using the Pythogoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Q.

The coordinates of the image of the origin O with respect to the straight line x+y+1=0 are

1. $(-\frac{1}{2},-\frac{1}{2})$

2. $(-2,-2)$

3. $(1,1)$

4. $(-1,-1)$

Q. Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.

Q.

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

1. $\frac{1}{h}+\frac{1}{k}=\frac{1}{3}$

2. $\frac{1}{h}-\frac{1}{k}=\frac{1}{3}$

3. $\frac{1}{k}-\frac{1}{h}=\frac{1}{3}$

4. $\frac{1}{k}-\frac{1}{h}=\frac{1}{7}$

Q.

The area of the triangle formed by the lines $x+y=3$ and angle bisectors of the pair of straight lines $x^2-y^2+2y=1$ is?

Q.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$36x^2+4y^2=144$

Q. Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.

Q.

Find the coordinate of the circumcenter of the triangle with vertices $A\left(2,5\right)$, $B\left(6,6\right)$ and $C\left(12,3\right)$.

Q. If the vertices of a triangle are $(1,2),(4,-6)$ and $(3,5)$, then the area (in sq. units) of the triangle is

1. $\frac{25}{2}$
2. $12$
3. $5$
4. $25$

Q. If the co-ordinates of two points A and B are (3, 4) and (5, -2) respectively, find the co-ordinates of any point P if PA=PB and Area of triangle PAB =10

1. (2, 7)

2. (0, 1)

3. (7, 2)

4. (1, 0)

Q. Area of the triangle formed by the points$\left((a+3)(a+4),a+3\right),\left((a+2)(a+3),(a+2)\right)\mathrm{and}\left((a+1)(a+2),(a+1)\right)$ is
(a) 25a²
(b) 5a²
(c) 24a²
(d) none of these

Q. If the area of the pentagon formed by the vertices $A(1,3),B(-2,5),C(-3,-1),D(0,-2)$ and $E=(2,t)$ is $\frac{45}{2}\text{sq. units}$, then possible value(s) of $t$ is/are

1. $-1$
2. $1$
3. $-99$
4. $89$

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. $x+2y-1=0$

Q.

Find the centre and length of the diagonal of the square formed by the lines $y=3,x=6,y=7andx=10$

1. (5, 8) and 4√2

2. (5, 8) and 2√2

3. (8, 5) and 2√2

4. (8, 5) and 4√2

5. (5, 8) and 4

Q.

Find the image of the point (3, 8) with respect to the line $x+3y=7$ assuming the line to be a plane mirror.

Q. Draw a quadrilateral in the Cartesian plane, whose vertices are $(-4,5),(0,7),(5,-5)$ and $(-4,-2)$. Also, find its area.