Area of Triangle Using Coordinates

Q. Let $P=(\frac{1}{x_p},p),Q=(\frac{1}{x_q},q)$ and $R=(\frac{1}{x_r},r)$, where $x_k\ne 0$ denotes the $k^{th}$term of an H.P. for $k\in N$. If the area formed by the points $P,Q$ and $R$ is $\lambda pqr$ sq. units, then the value of $\lambda$ is

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

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. $\frac{15}{8}$
2. $\frac{25}{4}$
3. $\frac{25}{8}$
4. $\frac{25}{16}$

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

1. $5$
2. $4$
3. $9$
4. $10$

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. $\frac{15}{8}$
2. $\frac{25}{4}$
3. $\frac{25}{8}$
4. $\frac{25}{16}$

Q. If the vertices of a triangle are $(t,t-2),$ $(t+2,t+2)$ and $(t+3,t),$ then the area (in sq. units) of the triangle is

1. $4$
2. $8$
3. $16$
4. Dependent on the value of $t$.

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. $\frac{15}{8}$
2. $\frac{25}{4}$
3. $\frac{25}{8}$
4. $\frac{25}{16}$

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.

If the vertices of a triangle be $(a{m}_1^2,2a{m}_1),(a{m}_2^2,2a{m}_2)and(a{m}_3^2,2a{m}_3)$, then the area of the triangle is

1. $a(m_2-m_3)(m_3-m_1)(m_1-m_2)$

2. $(m_2-m_3)(m_3-m_1)(m_1-m_2)$

3. $a^2(m_2-m_3)(m_3-m_1)(m_1-m_2)$

4. 4

Q. Let $OPQR$ be a square and $M$ and $N$ be the midpoints of the sides $PQ$ and $QR$ respectively. The ratio of the area of square to the triangle $OMN$ is

1. $4:1$
2. $2:1$
3. $8:3$
4. $7:3$

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. The points (k, –2k), (–k + 1, 2k) and
(–4 –k, 6 –2k) can't be collinear for any value of k.

1. True
2. False

Q. The coordinates of points $P,Q,R$ and $S$ are $(-3,5),(4,-2),(p,3p)$ and $(6,3)$ respectively, and the area of $△PQR$ and $△QRS$ are in ratio $2:3,$ then possible value of $p$ can be

1. $-\frac{5}{43}$
2. $\frac{3}{43}$
3. $\frac{46}{41}$
4. $\frac{45}{41}$

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 (0, –1) parallel to x ­– axis at C. The area of the triangle ABC is

1. 182sq. Units
2. 91 sq. Units
3. 48 sq. Units
4. 501 sq units

Q. Let A (h, k), B (1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which `k' can take is given by

1. {1, 3}
2. {0, 2}
3. {-1, 3}
4. {-3, -2}

Q. The points (k, –2k), (–k + 1, 2k) and
(–4 –k, 6 –2k) can't be collinear for any value of k.

1. True
2. False

Q. Let A (h, k), B (1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which `k' can take is given by

1. {1, 3}
2. {0, 2}
3. {-1, 3}
4. {-3, -2}

Q. If the vertices of a triangle are $(t,t-2),$ $(t+2,t+2)$ and $(t+3,t),$ then the area (in sq. units) of the triangle is

1. $4$
2. $8$
3. $16$
4. Dependent on the value of $t$.

Q.

Find the ratio in which the line segment joining the points $A\left(3,-3\right)$ and $B\left(-2,7\right)$ is divided by $x-axis$. Also find the coordinates of the point of division.

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. Let $PAB$ be a triangle in which $PA=PB$ and the coordinates of $A$ and $B$ are $(-1,-6)$ and $(-5,-2)$ respectively. If the area of $△PAB$ is $8$ square units, then the coordinates of $P$ are

1. $(-1,-2)$
2. $(-2,-3)$
3. $(-4,-5)$
4. $(-5,-6)$

Q. The point $A$ divides the line segment joining the points $(-5,1)$ and $(3,5)$ in the ratio $k:1$. The coordinates of points $B$ and $C$ are $(1,5)$ and $(7,-2)$ respectively. If the area of $△ABC$ is $2$ square units, then the number of values of $k$ is

1. $1$
2. $2$
3. $3$
4. $4$