More from Anant Ratan

Question 1 :
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is :

Question 2 :
If (a, b) is the mid-point of the line segment joining the points A (10, –6) and B (k, 4) and a – 2b = 18, find the distance AB.

Question 4 :
Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5).

Question 5 :
The points A (–1, 0), B (3, 1), C (2, 2) and D (–2, 1) are the vertices of a parallelogram. State true or false.

Question 6 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd4273b230584979a25.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. What is the distance between both the flags?

Question 7 :
Point P (5, –3) is one of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5). State true or false.

Question 8 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd2273b230584979a22.png ' /> The above image shows the arrangement of desks in a classroom. Ashima, Bharti and Camella are seated at A $\left(3, 1\right)$ , B $\left(6, 4\right)$ and C $\left(8, 6\right)$ respectively. Do you think they are seated in a line?

Question 9 :
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 10 :
If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is :

Question 11 :
If Q $\left(0, 1\right)$ is equidistant from P $\left(5, –3\right)$ and R $\left(4, 6\right)$. Find the distance PR.

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4c273b230584979918.PNG' /> Look at the above image. In a classroom, 4 friends are seated at the points A, B, C and D as shown in figure. 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 which of them is correct.

Question 13 :
Let X, Y and Z be the points which divide the line segment joining A $\left(– 2, 2\right)$ and B $\left(2, 8\right)$ into four equal parts. Find the coordinates of X.

Question 14 :
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 15 :
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.

Question 16 :
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 17 :
If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then :

Question 18 :
Determine, if the points (1,5), (2,3) and (-2 ,-11) are collinear.

Question 19 :
If $\left(1, 2\right)$, $\left(4, y\right)$, $\left(x, 6\right)$ and $\left(3, 5\right)$ are the vertices of a parallelogram taken in order, find x and y.

Question 20 :
Find the area of a triangle formed by the points A $\left(5, 2\right)$, B $\left(4, 7\right)$ and C $\left(7, – 4\right)$.

Question 21 :
The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5). State true or false.

Question 22 :
The point A (2, 7) lies on the perpendicular bisector of line segment joining the points P (6, 5) and Q (0, – 4). State true or false.

Question 23 :
The points (4, 5), (7, 6) and (6, 3) are collinear. State true or false.

Question 24 :
Find the value of ‘k’, for which the points $\left(8, 1\right)$, $\left(k, – 4\right)$ and $\left(2, –5\right)$ are collinear.

Question 25 :
Find the distance between the points $\left(0, 0\right)$ and $\left(36, 15\right)$.

Question 26 :
Find the point on the x-axis which is equidistant from $\left(2, –5\right)$ and $\left(–2, 9\right)$.

Question 28 :
If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x, y) and x + y – 10 = 0, find the value of k.

Question 29 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd8273b230584979a2a.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 the area of ∆PQR if A is the Origin?

Question 30 :
Find the values of k if the points A (k + 1, 2k), B (3k, 2k + 3) and C (5k – 1, 5k) are collinear.