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).
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)
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.
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.
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 AD and BE of $\triangle\text{ABC}$ 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).
Find the ratio in which the point $P(x, 2)$ divides the join of $A(12, 5)$ and $B(4, -3).$
View full solution →In what ratio does the line x - y - 2 = 0 divide the line segment joining the points A(3, -1) and B(8, 9)
For what value of $x$ are the points $A(-3, 12), B(7, 6)$ and $C(x, 9)$ colinear?
View full solution →If the points $P(-3, 9), Q(a, b)$ and $R(4, -5)$ are collinear and $a + b = 1$, find the values of $a$ and $b$.
View full solution →Prove that the points $A(a, 0), B(0, b)$ and $C(1, 1)$ are collinear, if $\frac{1}{\text{a}{}}+\frac{1}{\text{b}}=1.$
View full solution →Using the distance formula, show taht the given points are collinear:
(-1, -1), (2, 3) and (8, 11)