Two Point Form of a Line

Q. The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Q. Find the equation of the line which intersects the x -axis at a distance of 3 units to the left of origin with slope –2.

Q. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (−4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

Q. The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?

Q. P ( a, b ) is the mid-point of a line segment between axes. Show that equation of the line is

Q. Find the equation of the line which passes through the points (–1, 1) and (2, –4).

Q.

If $O$ is the origin and $A$ is a point on the curve $y^2=4x$. Then, the locus of the mid - point of $OA$, is

1. $x^2=4y$

2. $x^2=2y$

3. $x^2=16y$

4. $y^2=2x$

Q. The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

Q. Find the perpendicular distance from the origin to the line joining the points

Q.

If the sum of the slopes of the lines represented by the equation $x^2-2xytanA-y^2=0$ be 4, then $\angle A$ =

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2. 

3. 

4. 

Q.

One bisector of the angle between the lines given by $a(x-1{)}^2+2h(x-1)y+b{y}^2=0$ is 2x + y - 2 = 0.The other bisector is

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2. 

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4. 

Q.

The points $z_1,z_2,z_3,z_4$ in the complex plane are the vertices of a parallelogram taken in order, if and only if

1. z₁+z₄=z₂+z₃

2. z₁+z₃=z₂+z₄

3. None of these

4. z₁+z₂=z₃+z₄

Q.

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

1. x - 9y - 22 = 0

2. 21x + y + 13 = 0

3. 2x + y - 6 = 0

4. 11x - 4y + 43 = 0

Q. In the triangle ABC with vertices A (2, 3), B (4, – 1) and C (1, 2), find the equation and length of altitude from the vertex A.

Q. The owner of a milk store finds that, he can sell $980$ litres of milk each week at Rs $14$/litre and $1220$ litres of milk each week at Rs $16$/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs $17$/litre

Q.

Pick the correct plot for the function $y=x^2-2x+6$

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2. 

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4. 
   
   

Q. Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?

Q. If points $(x_1,4),(-2,y_1)$ lie on the line joining the points $(2,-1)$ and $(5,-3),$ then the value of $2x_1+9y_1$ is

Q. The equation of the internal bisector of the angle A of a triangle ABC whose vertices are A(4, 3), B(0, 0) and C(2, 3) is .

1. x-3y+5=0
2. x+3y-5=0
3. 3x-y-9=0
4. 3x+y-9=0

Q. Let $PS$ be the median of a triangle with vertices $P(2,2),$ $Q(6,-1)$ and $R(7,3).$ The equation of the line passing through $(1,-1)$ and parallel to $PS$ is

1. $2x-9y-7=0$
2. $2x-9y-11=0$
3. $2x+9y-11=0$
4. $2x+9y+7=0$

Q. Find the angle between the x -axis and the line joining the points (3, –1) and (4, –2).

Q. The line through the points ( h , 3) and (4, 1) intersects the line 7 x – 9 y – 19 = 0 . at right angle. Find the value of h .

Q. Find $x$ and $y$ intercepts of the given line:

1. $a=\frac{11}{2},b=-11$
2. $a=\frac{11}{2},b=11$
3. $a=\frac{11}{2},b=-11$
4. $a=\frac{2}{11},b=-11$