Question 1 :
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 2 :
The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, –9) and has diameter 10$\sqrt 2$ units.

Question 3 :
Point P (0, 2) is the point of intersection of y–axis and perpendicular bisector of line segment joining the points A (–1, 1) and B (3, 3). State true or false.

Question 4 :
The distance between the points A (0, 6) and B (0, –2) is :

Question 5 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd3273b230584979a24.JPG' /> In a classroom, 4 friends are seated at the points A, B, C and D as shown in the above image. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find out who is correct.

Question 6 :
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 7 :
A circle has its centre at the origin and a point P (5, 0) lies on it. The point Q (6, 8) lies outside the circle. State true or false.

Question 8 :
In what ratio does the point $\left(– 4, 6\right)$ divide the line segment joining the points A $\left(– 6, 10\right)$ and B $\left(3, –8\right)$?

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd8273b230584979a2b.png ' /> The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the above image. The students are to sow seeds of flowering plants on the remaining area of the plot.What will be your observation regarding the areas of the triangles when A and C are taken as origins, respectively ?

Question 10 :
Find the point on the x-axis which is equidistant from $\left(2, –5\right)$ and $\left(–2, 9\right)$.