Question 1 :
The points (4, 5), (7, 6) and (6, 3) are collinear. State true or false.
Question 2 :
Find the centre of a circle passing through the points $\left(6, – 6\right)$, $\left(3, – 7\right)$ and $\left(3, 3\right)$.
Question 3 :
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 4 :
Point P (– 4, 2) lies on the line segment joining the points A (– 4, 6) and B (– 4, – 6). State true or false.
Question 5 :
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 6 :
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 7 :
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceless triangle.
Question 8 :
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 9 :
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 10 :
Name the type of quadrilateral formed by the points $\left(4, 5\right)$, $\left(7, 6\right)$, $\left(4, 3\right)$ and $\left(1, 2\right)$
Question 11 :
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 12 :
Name the type of quadrilateral formed, if any, by the following points (4,5) , (7,6) , (4,3) , (1,2).
Question 13 :
Find the area of a rhombus if its vertices are $\left(3, 0\right)$, $\left(4, 5\right)$, $\left(– 1, 4\right)$ and $\left(– 2, – 1\right)$ taken in order.
Question 14 :
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 15 :
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 16 :
If the points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram, find the value of a.
Question 17 :
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 18 :
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 19 :
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are $\left(0, –1\right)$ ,$\left(2, 1\right)$ and $\left(0, 3\right)$.
Question 20 : <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 21 :
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 22 :
Name the type of quadrilateral formed, if any, by the following points (-3,5) , (3,1) , (0,3) , (-1,-4).
Question 23 :
If A $\left(–5, 7\right)$, B $\left(– 4, –5\right)$, C $\left(–1, –6\right)$ and D $\left(4, 5\right)$ are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
Question 24 :
If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then :
Question 25 :
Find the distance between the points (0, 0) and (36, 15).
Question 26 :
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 27 :
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 28 :
The points (0, 5), (0, –9) and (3, 6) are collinear. State true or false.
Question 29 :
Find the area of the triangle whose vertices are $\left(0, –1\right)$, $\left(2, 1\right)$ and $\left(0, 3\right)$.
Question 30 :
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 31 :
The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the :
Question 32 :
The distance between the points A (0, 6) and B (0, –2) is :
Question 33 :
Find the distance between the following pair of points: (2,3) , (4,1).
Question 34 :
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 35 :
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 36 :
If the distance between the points (4, p) and (1, 0) is 5, then the value of p is :
Question 37 :
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 38 :
Find the area of a triangle whose vertices are $\left(1, –1\right)$, $\left(– 4, 6\right)$ and $\left(–3, –5\right)$.
Question 39 : <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 40 :
Find the distance between the following pair of points: (a,b) , (-a,-b).
Question 41 :
The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is :
Question 42 :
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 43 :
The distance between the points (0, 5) and (–5, 0) is :
Question 44 :
Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
Question 45 :
What is the distance between two points P ($x_1,y_1$) and Q ($x_2,y_2$) ?
Question 46 :
The distance of the point P (–6, 8) from the origin is :
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 :
Point P (0, –7) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A (–1, 0) and B (7, –6). State true or false.
Question 49 :
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 50 :
If the point A (2, – 4) is equidistant from P (3, 8) and Q (–10, y), find distance PQ.
