Sample QuestionsCo-ordinate Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the line segment joining the points $(3, -4)$ and $(1, 2)$ is trisected at points $P(a, -2)$ and $\text{Q}\Big(\frac{5}{3},\text{b}\Big).$ Then,
- A
$\text{a}=\frac{8}{3},\text{b}=\frac{2}{3}$
- ✓
$\text{a}=\frac{7}{3},\text{b}=0$
- C
$\text{a}=\frac{1}{3},\text{b}=1$
- D
$\text{a}=\frac{2}{3},\text{b}=\frac{1}{3}$
Answer: B.
View full solution →If points $(t, 2t), (-2, 6)$ and $(3, 1)$ are collinear, then $t =$
- A
$\frac{3}{4}$
- ✓
$\frac{4}{3}$
- C
$\frac{5}{3}$
- D
$\frac{3}{5}$
Answer: B.
View full solution →The distance between the points $(\text{a}\cos25^\circ,0)$ and $(0,\text{a}\cos65^\circ)$ is:
Answer: A.
View full solution →The coordinates of the fourth vertex of the rectangle formed by the points $(0, 0), (2, 0), (0, 3)$ are,
- A
$(3, 0)$
- B
$(0, 2)$
- ✓
$(-2, 3)$
- D
$(3, 2)$
Answer: C.
View full solution →A line segment is of length $10$ units. If the coordinates of its one end are $(2, -3)$ and the abscissa of the other end is $10$, then its ordinate is:
- A
$9, 6$
- ✓
$3, -9$
- C
$-3, 9$
- D
$9, -6$
Answer: B.
View full solution →What is the distance between the points $A(c, 0)$ and $B(0, -c)?$
View full solution →Find the value of a so that the point $(3, a)$ lies on the line represented by $2x - 3y + 5 = 0$
View full solution →On which axis do the following points lie$?$
$S(0, 5).$
View full solution →Find the distance between the points $\Big(\frac{-8}{5},2\Big)$ and $\Big(\frac{2}{5},2\Big).$
View full solution →If $P(2, 6)$ is the mid-point of the line segment joining $A(6, 5)$ and $B(4, y),$ find $y.$
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 $\Big(\frac{7}{2},\text{y}\Big),$ find the value of $y.$
View full solution →Find the distance of the point $(1, 2)$ from the mid-point of the line segment joining the points $(6, 8)$ and $(2, 4).$
View full solution →In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at $A(3, 1), B(6, 4)$ and $C(8, 6).$ Do you think they are seated in a line$?$
View full solution →Show that the points $(-3, 2), (-5, -5), (2, -3)$ and $(4, 4)$ are the vertices of a rhombus. Find the area of this rhombus.
View full solution →If the points $A(-1, -4), B(b, c)$ and $C(5, -1)$ are collinear and $2b + c = 4,$ find the values of $b$ and $c.$
View full solution →Four points $A(6, 3), B(-3, 5), C(4, -2)$ and $D(x, 3x)$ are given in such a way that $\frac{\triangle\text{DBC}}{\triangle\text{ABC}}=\frac{1}{2},$ find $x.$
View full solution →Prove that the points $(3, -2), (4, 0), (6, -3)$ and $(5, -5)$ are the vertices of a parallelogram.
View full solution →$ABCD$ is a rectangle formed by joining the points $A(-1, -1), B(-1, 4) C(5, 4)$ and $D(5, -1). P, Q, R$ and $S$ are the mid-points of sides $AB, BC, CD$ and $DA$ respectively. Is the quadrilateral $PQRS$ a square? a rectangle? or a rhombus? Justify your answer.
View full solution →Find the centre of the circle passing through $(5, -8), (2, -9)$ and $(2, 1).$
View full solution →If the points $(-2, -1), (1, 0), (x, 3)$ and $(1, y)$ form a parallelogram, find the values of $x$ and $y.$
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