Question 1 :
Find the value of k if the points A $\left(2, 3\right)$, B $\left(4, k\right)$ and C $\left(6, –3\right)$ are collinear.

Question 2 :
The vertices of a ∆ABC are A $\left(4, 6\right)$, B $\left(1, 5\right)$ and C $\left(7, 2\right)$. A line is drawn to intersect sides AB and AC at D and E respectively, such that $\frac{AD}{AB}$=$\frac{AE}{AC}$=$\frac{1}{4}$. Calculate the ratio of the area of the triangle ADE to the area of the triangle ABC.

Question 3 :
Find the area of the triangle whose vertices are $\left(0, –1\right)$, $\left(2, 1\right)$ and $\left(0, 3\right)$.

Question 4 :
If Q $\left(0, 1\right)$ is equidistant from P $\left(5, –3\right)$ and R $\left(4, 6\right)$. Find the distance QR.

Question 5 :
What is the relation between x and y such that the point $\left(x , y\right)$ is equidistant from the points $\left(7, 1\right)$ and $\left(3, 5\right)$?

Question 6 :
Find the ratio in which the point P ($\frac {3}{4}$,$\frac {5}{12}$) divides the line segment joining the points A ($\frac {1}{2}$,$\frac {3}{2}$) and B (2, –5).

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd5273b230584979a26.JPG' /> To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the above image. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance AD on the eighth line and posts a red flag. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Question 8 :
Find the coordinates of the points of trisection (i.e., points dividing in three equal parts) of the line segment joining the points A $\left(2, – 2\right)$ and B $\left(– 7, 4\right)$.

Question 9 :
If A and B are $\left(– 2, – 2\right)$ and $\left(2, – 4\right)$, respectively, find the coordinates of P such that AP = $\frac{3}{7}$ AB and P lies on the line segment AB.

Question 10 :
Find the area of the triangle ABC with A (1, –4) and the mid-points of sides through A being (2, – 1) and (0, – 1).

Question 11 :
∆ ABC with vertices A (–2, 0), B (2, 0) and C (0, 2) is similar to ∆ DEF with vertices D (–4, 0) E (4, 0) and F (0, 4). State true or false.

Question 12 :
A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ∆ ADE.

Question 13 :
Find the area of the triangle formed by the points P $\left(–1.5, 3\right)$, Q $\left(6, –2\right)$ and R $\left(–3, 4\right)$.

Question 14 :
Find the area of the quadrilateral whose vertices, taken in order, are $\left(– 4, – 2\right)$, $\left(– 3, – 5\right)$, $\left(3, – 2\right)$ and $\left(2, 3\right)$.

Question 15 :
The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is :

Question 16 :
Let A $\left(4, 2\right)$ , B $\left(6, 5\right)$ and C $\left(1, 4\right)$ be the vertices of ∆ABC.The median of A meets BC at D. Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1

Question 17 :
A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively :

Question 18 :
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).

Question 19 :
What is the distance between two points P ($x_1,y_1$) and Q ($x_2,y_2$) ?

Question 20 :
Find the distance between the following pair of points: (2,3) , (4,1).

Question 21 :
The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a :

Question 22 :
The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is :

Question 23 :
The vertices of a ∆ABC are A $\left(4, 6\right)$, B$\left(1, 5\right)$ and C $\left(7, 2\right)$. A line is drawn to intersect sides AB and AC at D and E respectively, such that $\frac{AD}{AB}$=$\frac{AE}{AC}$=$\frac{1}{4}$. Calculate the area of triangle ABC.

Question 24 :
Find the area of the triangle whose vertices are $\left(-5, -1\right)$, $\left(3, -5\right)$, $\left(5, 2\right)$

Question 25 :
The points (–4, 0), (4, 0), (0, 3) are the vertices of a :

Question 26 :
Name the type of quadrilateral formed by the points $\left(–3, 5\right)$, $\left(3, 1\right)$, $\left(0, 3\right)$ and $\left(–1, – 4\right)$.

Question 27 :
Find the values of k if the points A (k + 1, 2k), B (3k, 2k + 3) and C (5k – 1, 5k) are collinear.

Question 28 :
What is the ratio in which the line $2x + y – 4 = 0$ divides the line segment joining the points A $\left(2, – 2\right)$ and B $\left(3, 7\right)$

Question 29 :
You have studied the median of a triangle divides it into two triangles of equal areas. Is the statement true for ∆ ABC whose vertices are A $\left(4, – 6\right)$, B $\left(3, –2\right)$ and C $\left(5, 2\right)$?

Question 30 :
If Q $\left(0, 1\right)$ is equidistant from P $\left(5, –3\right)$ and R $\left(x, 6\right)$, find the values of x.