Sample QuestionsDistance and Section Formulae questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the midpoint of the line segment joining the following pair of point :
$( a+3, 5b), (3a-1, 3b +4).$
View full solution →Find the midpoint of the line segment joining the following pair of point :
$(3a-2b, Sa+7b)$ and $(a+4b, a-3b)$
View full solution →Find the midpoint of the line segment joining the following pair of point :
$(a+b, b-a)$ and $(a-b, a+b)$
View full solution →Find the midpoint of the line segment joining the following pair of point :
$( -3, 5)$ and $(9, -9)$
View full solution →Find the midpoint of the line segment joining the following pair of point :
$(4,7)$ and $(10,15)$
View full solution →Find the length of the median through the vertex A of triangle ABC whose vertices are A (7, -3), B(S, 3) and C(3, -1).
Three consecutive vertices of a parallelogram ABCD are $A(S, 5), B(-7, -5)$ and $C(-5, 5).$ Find the coordinates of the fourth vertex D.
View full solution →P( -2, 5), Q(3, 6 ), R( -4, 3) and S(-9, 2) are the vertices of a quadrilateral. Find the coordinates of the midpoints of the diagonals PR and QS. Give a special name to the quadrilateral.
The coordinates of the end points of the diameter of a circle are (3, 1) and (7, 11). Find the coordinates of the centre of the circle.
The mid point of the line segment joining the points $(p, 2)$ and $(3, 6)$ is $(2, q).$ Find the numerical values of a and b.
View full solution →If $(-3, 2), (1, -2)$ and $(5, 6)$ are the midpoints of the sides of a triangle, find the coordinates of the vertices of the triangle.
View full solution →If the midpoints of the sides ofa triangle are $(-2, 3), (4, -3), (4, 5),$ find its vertices.
View full solution →The points $(2, -1), (-1, 4)$ and $(-2, 2)$ are midpoints of the sides ofa triangle. Find its vertices.
View full solution →Let $A(-a, 0), B(0, a)$ and $C(\alpha, \beta)$ be the vertices of the $L 1 A B C$ and $G$ be its centroid. Prove that $G A^2+G B^2+G C^2=\frac{1}{3}\left(A B^2+B C^2+C A^2\right)$
View full solution →Prove that the points $A(-5, 4), B(-1, -2)$ and $C(S, 2)$ are the vertices of an isosceles right-angled triangle. Find the coordinates of D so that ABCD is a square.
View full solution →AB is a diameter of a circle with centre $0.$ If the ooordinates of $A$ and $0$ are $( 1, 4)$ and $(3, 6).$ Find the ooordinates of B and the length of the diameter.
View full solution →The midpoints of three sides of a triangle are $(1, 2), (2, -3)$ and $(3, 4).$ Find the centroid of the triangle.
View full solution →Two vertices of a triangle are $( -1, 4)$ and $(5, 2).$ If the centroid is $(0, 3),$ find the third vertex.
View full solution →The coordinates of the centroid I of triangle PQR are $(2, 5).$ If $Q = (-6, 5)$ and $R = (7, 8).$ Calculate the coordinates of vertex $P.$
View full solution →$A( 4, 2), B(-2, -6)$ and $C(l, 1)$ are the vertices of triangle ABC. Find its centroid and the length of the median through C.
View full solution →