Two Point Form

Q.

Find the equation of line joining the points $(1,-3)$ and $(4,-2).$

1. x + y - 2 = 0

2. x - 3y - 10 = 0

3. x + y + 1 = 0

4. 3x + y - 10 = 0

Q.

The equation of the line passing through $(2,0)$ and $(0,3)$ is $\frac{x}{2}+\frac{y}{3}=1$

1. False

2. True

Q.

The line joining the points $(2,3)$ and $(3,-1)$ passes through the point $(5,-9)$.

1. False

2. True

Q.

Find the slope of the line which passes through the points $A(4,-6)$ and $B(-2,-5)$.

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

1. 21x + y + 13 = 0
2. 2x + y - 6 = 0
3. 11x - 4y + 43 = 0

Q. Question 7 (iii)
Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.
(c) Find the coordinates of point Q and R on medians BE and CF respectively such that BQ : QE = 2:1 and CR:RF = 2:1.

Q.

The coordinates of the vertices of a parallelogram ABCD are A(x, y), B (5, 8), C (4, 7) and D (2, -4). Find the equation of diagonal BD.

1. 4x-y-12=0

2. 4x-2y-12=0

3. 4x-y-10=0

4. 8x-y-12=0

Q.

Find the equation of the line passing through the points (2, 3) and the point of intersection of the lines $4x-3y=7$ and $3x+4y+1=0$.

1. 4x-y-2=0

2. 4x+y-5=0

3. 4x-y-5=0

4. 4x-y+5=0

Q.

$(3,0)$ is a point on the line joining the points $(3x^2,6x)$ and $(3y^2,6y)$. Then,

1. $\frac{1}{x}=\frac{1}{y}$

2. $y=-x$

3. $xy=-1$

4. $xy=1$

Q.

The equation of a line passing through the intersection of lines x = 0 and y = 0 and through the point (2, 2) is ________.

1. y = –x + 2

2. y = x – 1

3. y = –x

4. y = x

Q. Solve the following equations.
$log(5-x)+log(3-x)=1.$

Q. Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).

Q. If the points (k, 2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, find the possible values of k.
$\left[4Marks\right]$

Q. If the points (k, 2-2k), (1-k, 2k) and (-k-4, 6-2k) lie on a line, then find the possible values of k.$\left[3Marks\right]$

Q.

Find the slope of the line that passes through the points (-1, 0) and (3, 8).

1. 0​​​​​
2. 1
3. 2
4. 4

Q. The slope of the line which is passing though (5, 6) and (6, 7) is

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

Q.

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear.

1. 1

2. -1

3. 4

4. -4

Q. Find the value of $y$ if the line passing through the points $(3,y)$ and $(2,7)$ is parallel to the line passing through the points $(-1,4)$ and $(0,6)$.

1. -9

2. 6

3. -6

4. 9

Q.

Find the equation of the line passing through the points (2, 3) and the point of intersection of the lines $4x-3y=7$ and $3x+4y+1=0$.

1. 4x-y+5=0

2. 4x-y-2=0

3. 4x+y-5=0

4. 4x-y-5=0

Q. The vertex points of a parabola is given by

1. $(\frac{b}{2a},\frac{4ac-b^2}{4a})$
2. $(\frac{-b}{2a},\frac{4ac-b^2}{4a})$
3. $(\frac{-b}{2a},\frac{4ac-b^2}{a})$
4. $(\frac{-b}{2a},\frac{4ac-b^2}{-a})$

Q.

Find the slope of the line that passes through the points (-1, 0) and (3, 8).

1. $\frac{1}{4}$

2. $\frac{1}{2}$

3. $2$

4. does not exist

Q. Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).

1. 3x-y+1=0

2. x+3y+7=0

3. 7x- y-11=0

4. 7x+y-11=0

Q. Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear.
$\left[2Marks\right]$

Q. Find the equations of the sides of the triangle, the coordinates of whose vertices are (1, 4), (2, -3) and (-1, -2).
$\left[3Mark\right]$

Q. If x = a and y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are respectively:
(A) 3 and 5
(B) 5 and 3
(C) 3 and 1
(D) –1 and –3