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 $A(4, 2), B(6, 5)$ and $C(1, 4)$ be the verteces of $\triangle\text{ABC}$ and $AD$ is a median, then the coordinates of $D$ are:
- A
$\Big(\frac{5}{2},3\Big)$
- B
$\Big(5,\frac{7}{2}\Big)$
- ✓
$\Big(\frac{7}{2},\frac{9}{2}\Big)$
- D
$\text{none of these}$
Answer: C.
View full solution →If the points $A(2, 3), B(5 , k)$ and $C(6, 7)$ are collinear then:
- A
$\text{k}=4$
- ✓
$\text{k}=6$
- C
$\text{k}=\frac{-3}{2}$
- D
$\text{k}=\frac{11}{4}$
Answer: B.
View full solution →Two vertices of $\triangle\text{ABC}$ are $A(-1, 4)$ and $B(5, 2)$ and its centroid is $G(0, -3)$. Then, the coordinates of $C$ are:
- A
$(4, 3)$
- B
$(4, 15)$
- ✓
$(-4, -15)$
- D
$(-15, -4)$
Answer: C.
View full solution →If $A(-1, 0), B(5, -2)$ and $C(8, 2)$ are the vertices of a $\triangle\text{ABC}$ then its centroid is:
- A
$(12, 0)$
- B
$(6, 0)$
- C
$(0, 6)$
- ✓
$(4, 0)$
Answer: D.
View full solution →In the given figure $P(5, -3)$ and $Q(3, y)$ are the points of teisection 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 →Find the distance between the points:
$A(1, -3)$ and $B(4, -6)$
View full solution →If the coordinates of points $A$ and $B$ are $(-2, -2)$ and $(2, -4)$ respectively, find the coordinates of the points $P$ such that $\text{AP}=\frac{3}{7}\text{AB},$ where $P$ lies on the line segment $AB$.
View full solution →Find the coordinate of the points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.
View full solution →Find the area of $\triangle\text{ABC}$ whose vertices are:
$A(3, 8), B(-4, 2)$ and $C(5, -1)$
View full solution →Find the distance between the points:
$A(-6, -4)$ and $B(9, -12)$.
View full solution →Find the coordinate of the point equidistant from three given points $A(5, 3), B(5, -5)$ and $C(1, -5).$
View full solution →Show that the following points are the vertices of a rectangle:
$A(-4, -1), B(-2, -4), C(4, 0)$ and $D(2, 3)$
View full solution →Show taht the following points are collinear:
$A(2, -2), B(-3, 8)$ and $C(-1, 4)$
View full solution →If three consecutive vertices of a parallelogram $ABCD$ are $A(1, -2), B(3, 6)$ and $C(5, 10)$, find its fourth vertex $D.$
View full solution →$ABCD$ is a rectangle formed by points $A(-1, -1), B(-1, 4), C(5, 4)$ and $D(5, -1).$ If $P, Q, R$ and $S$ be the midpoints of $AB, BC, CD$ and $DA$ respectively, show that $PQRS$ is a rhombus.
View full solution →Find the centroid of $\triangle\text{ABC}$ whose vertices are $A(2, 2), B(-4, -4)$ and $C(5, -8).$
View full solution →If the point $A(0, 2)$ is equidistant from the points $B(3, p)$ and $C(p, 5)$, find $P.$
View full solution →Find the lengths of the medians $A D$ and $B E$ of $\triangle A B C$ whose vertices are $A(7,-3), B(5,3)$ and $C(3,1)$.
View full solution →Find the coordinates of a point $A$, where $AB$ is a diameter of a circle with center $C(2, -3)$ and the other end of the diameter is $B(1, 4).$
View full solution →Find the ratio in which the point $P(x, 2)$ divides the join of $A(12,5)$ and $B(4,-3)$.
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