Question 2 :
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 3 :
The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is :
Question 4 :
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 5 :
The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is :
Question 6 :
Name the type of quadrilateral formed, if any, by the following points (-3,5) , (3,1) , (0,3) , (-1,-4).
Question 7 : <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 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd5273b230584979a26.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. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Question 9 :
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 10 :
The points A (–1, –2), B (4, 3), C (2, 5) and D (–3, 0) in that order form a rectangle. State true or false.
Question 11 :
The distance of a point from the y-axis is called its x-coordinate, or abscissa. TRUE or FALSE ?
Question 12 :
Find the area of the triangle whose vertices are $\left(2, 3\right)$, $\left(–1, 0\right)$, $\left(2, – 4\right)$
Question 13 :
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 14 :
What are the coordinates of the point P which divides the line segment joining the points A ($x_1, y_1$) and B ($x_2, y_2$) internally in the ratio $m_1 : m_2$ ?
Question 15 :
If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then :
Question 16 :
Name the type of quadrilateral formed, if any, by the following points (4,5) , (7,6) , (4,3) , (1,2).
Question 17 :
Find the values of k if the points A (k + 1, 2k), B (3k, 2k + 3) and C (5k – 1, 5k) are collinear.
Question 18 : <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 19 :
Find the coordinates of the point which divides the line segment joining the points $\left(4, – 3\right)$ and $\left(8, 5\right)$ in the ratio 3 : 1 internally.
Question 20 :
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 21 :
Name the type of quadrilateral formed by the points $\left(-1,-2\right)$, $\left(1,0\right)$, $\left(-1,2\right)$ and $\left(-3,0\right)$.
Question 22 :
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Question 23 :
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 24 :
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 25 :
The distance of the point P (–6, 8) from the origin is :
Question 26 :
Name the type of triangle formed by the points $\left(5, – 2\right)$, $\left(6, 4\right)$ and $\left(7, – 2\right)$.
Question 27 :
Determine, if the points (1,5), (2,3) and (-2 ,-11) are collinear.
Question 28 :
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Question 29 :
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 30 :
Name the type of triangle PQR formed by the points P ($\sqrt 2$,$\sqrt 2$) , Q ($-\sqrt 2$,$-\sqrt 2$) and R ($-\sqrt 6$,$\sqrt 6$) .
Question 31 :
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 33 :
Find the coordinates of the points of trisection of the line segment joining $\left(4, -1\right)$ and $\left(-2, -3\right)$.
Question 34 :
The distance of the point P (2, 3) from the x-axis is :
Question 35 : <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 36 :
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 37 :
The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a :
Question 38 :
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 39 :
The points (0, 5), (0, –9) and (3, 6) are collinear. State true or false.
Question 40 :
What are the coordinates of the mid-point of the line segment joining the points P ($x_1,y_1$) and Q ($x_2,y_2$) ?
Question 41 :
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 42 :
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 43 :
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 value of k.
Question 44 :
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 45 :
Find the ratio in which the line segment joining the points $\left(– 3, 10\right)$ and $\left(6, – 8\right)$ is divided by $\left(– 1, 6\right)$.
Question 46 :
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 47 :
What is the distance of a point P (x,y) from the origin ?
Question 48 :
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 49 :
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 50 :
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.
