If the points $A (x, 2), B(-3,-4)$ and $C (7,-5)$ are collinear, then the value of $x$ is:
- ✓$-63$
- B$63$
- C$60$
- D$-60$
Answer: A.
View full solution →Question types
Coordinate Geometry question types
100 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
100
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
47 Q→021 Marks Question
3 Q→032 Marks Questions
16 Q→043 Marks Question
25 Q→055 Marks Questions
8 Q→06Case study (4 Marks)
1 Q→Sample Questions
Coordinate Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
ABCD is a rectangle whose three vertices are B $(4,0), C(4,3)$ and $D(0,3)$. The length of one of its diagonals is
- ✓5
- B4
- C3
- D25
Answer: A.
View full solution →In Fig, find the area of triangle $\text{ABC}\ ($in sq. units$)$ is:
- A$15$
- B$10$
- ✓$7.5$
- D$2.5$
Answer: C.
View full solution →In Figure, $P (5,-3)$ and $Q (3, y)$ are the points of trisection of the line segment joining $A(7,-2)$ and $B (1,-5)$. Then $y$ equals?
- A$2$
- B$4$
- ✓$-4$
- D$-\frac{5}{2}$
Answer: C.
View full solution →The distance of the point $(-3,4)$ from the $x$-axis is
- A3
- B-3
- ✓4
- D5
Answer: C.
View full solution →If the distance between the points $(4, k)$ and $(1,0)$ is $5 ,$ then what can be the possible values of $k$ ?
View full solution →If $\operatorname{ar}(\triangle PQR )$ is zero, then the points $P , Q$ and $R$ are $\qquad$
View full solution →Find the distance between the points $(a ,b)$ and $(-a,-b)$.
View full solution →If the distances of $P ( x , y )$ from $A (5,1)$ and $B (-1,5)$ are equal, then prove that $3 x =2 y $
View full solution →A line intersects the $y-$axis and $x-$axis at the points $P$ and $Q$ respectively. If $(2,-5)$ is the mid$-$point of $PQ$, then find the coordinates of $P$ and $Q$.
View full solution →Prove that the points $(3,0),(6,4)$ and $(-1,3)$ are the vertices of a right angled isosceles triangle.
View full solution →Let $P$ and $Q$ be the points of trisection of the line segment joining the points $A (2,-2)$ and $B (-7,4)$ such that $P$ is nearer to $A$ . Find the coordinates of $P$ and $Q$.
View full solution →The $x-$ coordinate of a point $P$ is twice its $y$ coordinate. If $P$ is equidistant from $Q(2,-5)$ and $R(-3,6),$ find the coordinates of $P$.
View full solution →The area of a triangle is $5$ sq units. Two of its vertices are $(2,1)$ and $(3,-2)$. If the third vertex is $\left(\frac{7}{2}, y\right)$, find the value of $y$.
View full solution →Show that $\triangle A B C$, whereA $(-2,0), B (2,0), C (0,2)$ and $\triangle P Q R$ where $(-4,0), Q(4,0) R(4,0)$ are similar triangles.
View full solution →In what ratio does the point $\left(\frac{24}{11}, y\right)$ divide the line segment joining the points $P (2,-2)$ and $Q(3,7)$ ? Also find the value of $y$
View full solution →In the given figure, $\text{ABC}$ is a triangle coordinates of whose vertex $A$ are $(0,-1) D$ and E respectively are the mid $-$ points of the sides $A B$ and $A C$ and their coordinates are $(1,0)$ and $(0,1)$ respectively. If $F$ is the mid $-$ point of $B C$, find the areas of $\triangle A B C$ and $\triangle D E F$.
View full solution →If the point $P(x, y)$ is equidistant from the points $A ( a + b , a - b )$ and $B ( a - b , a + b )$ Prove that $bx = ay$
View full solution →If $a \neq b \neq 0$, prove that the points $\left(a, a^2\right),\left(b, b^2\right)$, $(0,0)$ will not be collinear.
View full solution →If the points $A(k+1,2 k), B(3 k, 2 k+3)$ and $C(5 k-1,5 k)$ are collinear, then find the value of $k$.
View full solution →
Find the values of so that the area of the triangle with vertices $(1,-1),(-4,2 k)$ and $(-k,-5)$ is $24$ square units.
View full solution →If $A(-4,8), B(-3,-4), C(0,-5)$ and $D(5,6)$ are the vertices of a quadrilateral $A B C D$, find its area.
View full solution →Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play $"\text{PUBG}"$ can get easily stressed out. To raise social awareness about ill effects of playing $\text{PUBG},$ a school decided to start $'\text{BAN PUBG}\ '$ campaign, in which student are asked to prepare campaign board in the shape of a rectangle. One such campaign board made by class $X$ student of the school is shown in the figure.
Based on the above information, answer the following questions:
$(i)$ Find the coordinates of the point of intersection of diagonals $AC$ and $BD$ .
$(ii)$ Find the length of the diagonal $AC$ .
$(iii)\ (a$) Find the area of the campaign Board $\text{ABCD}$ .
OR
$(b)$ Find the ratio of the length of side $A B$ to the length of the diagonal $AC$.
View full solution →Based on the above information, answer the following questions:
$(i)$ Find the coordinates of the point of intersection of diagonals $AC$ and $BD$ .
$(ii)$ Find the length of the diagonal $AC$ .
$(iii)\ (a$) Find the area of the campaign Board $\text{ABCD}$ .
OR
$(b)$ Find the ratio of the length of side $A B$ to the length of the diagonal $AC$.
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