Question 1 :
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 2 :
Let A $\left(4, 2\right)$ , B $\left(6, 5\right)$ and C $\left(1, 4\right)$ be the vertices of ∆ABC. The median from A meets BC at D. Find the coordinates of the point D.

Question 3 :
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 4 :
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 the point P on AD such that AP : PD = 2 : 1

Question 5 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd5273b230584979a27.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.Taking A as origin, the coordinates of the vertices of the triangle are $\left(4,6\right)$ , $\left(3,2\right)$ and $\left(6,5\right)$.Are the coordinates correct?

Question 6 :
ABCD is a rectangle formed by the points A $\left(–1, –1\right)$, B $\left(– 1, 4\right)$, C $\left(5, 4\right)$ and D $\left(5, – 1\right)$. P, Q,R and S are the mid-points of AB, BC, CD and DA respectively. Name the type of quadrilateral.

Question 7 :
If A $\left(x_1, y_1\right)$, B $\left(x_2, y_2\right)$ and C $\left(x_3,y_3\right)$ are the vertices of ∆ABC, find the coordinates of the centroid of the triangle.

Question 8 :
The two opposite vertices of a square are $\left(–1, 2\right)$ and $\left(3, 2\right)$. Find the coordinates of the other two vertices.

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd6273b230584979a28.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 co-ordinates of the vertices of ∆PQR if C is the Origin?

Question 10 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd7273b230584979a29.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 C is the Origin?