Triangle in Rectangular Cartesian Coordinates

Q.

A man running in a racecourse notes that the sum of the distances of the two flag posts from him is always 10 m, and the distance between the flag posts is 8 m. Find the equation of the path traced by the man.

Q. Let $A(0,1),B(1,1),C(1,-1)$ and $D(-1,0)$ be four points. If $P$ is any other point, then the minimum value of $PA+PB+PC+PD$ is equal to

1. $\sqrt{5}$
2. $2\sqrt{5}$
3. $3\sqrt{5}$
4. $4\sqrt{5}$

Q.

If ∝ and β are roots of $x^2$ + ax - b = 0 and γ, δ​ arethe roots of $x^2$ + ax + b = 0, then (α-γ) (β-δ) (α-δ) (β-γ)

1. 2b²

2. 4b²

3. b

4. 2b

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 equations of the two sides of a triangle are $3x-2y+6=0$ and $4x+5y-20=0$ respectively. If the orthocentre of the triangle is (1, 1), find the equation of third side.

Q. The base of an equilateral triangle with side 2 a lies along they y -axis such that the mid point of the base is at the origin. Find vertices of the triangle.

Q. A(-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle. is the equation of the median through (-1, 8).

1. 11x - 4y + 43 = 0
2. x - 9y - 22 = 0
3. 21x + y + 13 = 0

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 square unit, then the set of values which ${}^{\prime }{k}^{\prime }$ can take is given by

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

Q. If the middle points of the sides BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and (-5, 7), then the equation of the side AB is

1. x-y-2=0
2. x-y+12=0
3. None of these
4. x+y-12=0

Q. If the coordinates of the vertices of the triangle ABC be (-1, 6), (- 3, - 9), and (5, -8) respectively, then the equation of the median through C is

1. 13x-14y-47=0
2. 13x-14y+47=0
3. 13x+14y+47=0
4. 13x+14y-47=0

Q.

The vertices of $\Delta PQR$ are P(2, 1), Q(-2, 3) and R(4, 5). Find equation of the median through the vertex R.

Q. The vertices of $\Delta PQR$ are $P(2,1),Q(-2,3)$ and $R(4,5)$. Find equation of the median through the vertex $R$.

Q. If the coordinates of the vertices of the triangle ABC be (-1, 6), (- 3, - 9), and (5, -8) respectively, then the equation of the median through C is

1. 13x-14y+47=0
2. 13x+14y+47=0
3. 13x+14y-47=0
4. 13x-14y-47=0