Question 1 :
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 2 : <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 3 :
Points A (3, 1), B (12, –2) and C (0, 2) cannot be the vertices of a triangle. State true or false.
Question 4 : <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?
Question 5 :
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 6 :
Find the point of intersection in which the y-axis divides the line segment joining the points $\left(5, – 6\right)$ and $\left(–1, – 4\right)$.
Question 7 :
If P (9a – 2, –b) divides line segment joining A (3a + 1, –3) and B (8a, 5) in the ratio 3 : 1, find the value of a.
Question 8 :
The distance between the points (0, 5) and (–5, 0) is :
Question 9 :
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 10 : <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 11 :
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 12 :
The points A (2, 9), B (a, 5) and C (5, 5) are the vertices of a triangle ABC right angled at B. Find the values of a and hence the area of ∆ABC.
Question 13 :
Find the distance between the following pair of points: (a,b) , (-a,-b).
Question 14 :
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 15 :
Find the value of a, if the distance between the points A (–3, –14) and B (a, –5) is 9 units.
Question 16 :
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 17 :
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
Question 18 :
Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
Question 19 :
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 Y.
Question 20 :
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 21 :
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Question 22 :
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 ADE.
Question 23 :
Find the distance between the points $\left(0, 0\right)$ and $\left(36, 15\right)$.
Question 24 :
Name the type of quadrilateral formed, if any, by the following points (-1,-2) , (1,0) , (-1,2) , (-3,0).
Question 25 :
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceless triangle.
Question 26 :
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 27 :
Find the area of the triangle whose vertices are $\left(2, 3\right)$, $\left(–1, 0\right)$, $\left(2, – 4\right)$
Question 28 :
Find the distance between the following pair of points: (2,3) , (4,1).
Question 29 :
What type of a quadrilateral do the points A (2, –2), B (7, 3), C (11, –1) and D (6, –6) taken in that order, form?
Question 30 :
Find the ratio in which the line segment joining A $\left(1, – 5\right)$ and B $\left(– 4, 5\right)$ is divided by the x-axis.
Question 31 :
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 Z.
Question 32 :
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 33 :
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 34 :
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 35 :
The points (4, 5), (7, 6) and (6, 3) are collinear. State true or false.
Question 36 :
If the distance between the points (4, p) and (1, 0) is 5, then the value of p is :
Question 37 :
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Question 38 :
If the point A (2, – 4) is equidistant from P (3, 8) and Q (–10, y), find distance PQ.
Question 39 :
Find the point on the x-axis which is equidistant from $\left(2, –5\right)$ and $\left(–2, 9\right)$.
Question 41 :
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 42 :
A circle drawn with origin as the centre passes through ($\frac {13}{2}$,0). The point which does not lie in the interior of the circle is :
Question 43 :
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 44 :
Name the type of the triangle formed by the points $\left(3,2\right)$ , $\left(2,3\right)$ , $\left(-2,-3\right)$.
Question 45 :
If the point A (2, – 4) is equidistant from P (3, 8) and Q (–10, y), find the values of y.
Question 46 :
Point P (– 4, 2) lies on the line segment joining the points A (– 4, 6) and B (– 4, – 6). State true or false.
Question 47 :
Find a relation between x and y such that the point $\left(x, y\right)$ is equidistant from the point $\left(3, 6\right)$ and $\left(– 3, 4\right)$.
Question 48 : <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 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b57273b230584979981.PNG' />
In the above figure, a ∆ AOB is shown. The coordinates of the point which is equidistant from the three vertices of the ∆ AOB is :
Question 50 :
Name the type of quadrilateral formed, if any, by the following points (-3,5) , (3,1) , (0,3) , (-1,-4).
