Find the co-ordinates of the centroid of a triangle ABC whose vertices are: $A(-1, 3), B(1, -1)$ and $C(5, 1)$
View full solution →Question types
Section and Mid-Point Formula question types
71 questions across 4 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
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Sample Questions
Section and Mid-Point Formula questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The mid-point of the segment AB, as shown in diagram, is C$(4, -3).$ Write down the co-ordinates of A and B.
View full solution →Find the image of the point A$(5,3)$ under reflection in the point P$(-1,3).$
View full solution →One end of the diameter of a circle is $(-2, 5).$ Find the co-ordinates of the other end of it, of the centre of the circle is $(2, -1)$
View full solution →In the given figure, $P (4, 2)$ is mid-point of line segment $AB.$ Find the co-ordinates of $A$ and $B.$
View full solution →AB is a diameter of a circle with centre $C = (-2, 5).$ If $A = (3, -7),$ find
(i) the length of radius $AC$
(ii) the coordinates of $B.$
View full solution →(i) the length of radius $AC$
(ii) the coordinates of $B.$
In what ratio is the line joining $A(0, 3)$ and $B (4, -1)$ divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis
View full solution →A line segment joining $A(-1,5/3)$ and $B (a, 5)$ is divided in the ratio $1 : 3$ at P, the point where the line segment AB intersects the y-axis.(i) calculate the value of ‘a’
(ii) Calculate the co-ordinates of ‘P’.
View full solution →(ii) Calculate the co-ordinates of ‘P’.
Find the co-ordinates of points of trisection of the line segment joining the point $(6, -9)$ and the origin.
View full solution →A (-4,2)2, B(0,2) and C (-2,-4) are the vertices of a triangle ABC. A,Q and R are mid-Points of sides BC,CA and AB respectively.Show that the centroid of Δ PQR is the same as the centroid of Δ ABC.
The points $(2, -1), (-1, 4)$ and $(-2, 2)$ are mid points of the sides of a triangle. Find its vertices
View full solution →Given a line segment AB joining the points A $(-4, 6)$ and B $(8, -3).$ Find:
(i) the ratio in which AB is divided by the y-axis
(ii) find the coordinates of the point of intersection
(iii) the length of AB.
View full solution →(i) the ratio in which AB is divided by the y-axis
(ii) find the coordinates of the point of intersection
(iii) the length of AB.
$A(-8, 0), B(0, 16)$ and $C(0, 0)$ are the verticals of a triangle $ABC.$ Point $P$ lies on $AB$ and $Q$ lies on $AC$ such that $AP : PB = 3 : 5$ and $AQ : QC = 3 : 5$ Show that : PQ =$\frac{3}{8}$ BC
View full solution →A(20, 0) and B(10, -20) are two fixed points Find the co-ordinates of the point P in AB such that : 3PB = AB, Also, find the co-ordinates of some other point Q in AB such that AB = 6 AQ.
A(3, 1), B(y, 4) and C(1, x) are vertices of a triangle ABC. P, Q and R are mid - points of sides BC, CA and AB respectively. Show that the centroid of ΔPQR is the same as the centroid ΔABC.
M is the mid-point of the line segment joining the points A(0,4) and B(6,0). M also divides the line segment OP in the ratio 1:3 find :
(a) co-ordinates of M
(b) Co-ordinates of P
(c) Length Of BP
(a) co-ordinates of M
(b) Co-ordinates of P
(c) Length Of BP
The line joining the points $(2,1)$ and $(5,-8)$ is trisected at the point $P$ and $Q,$ point $P$ lies on the line $2 x-y+k=0$, find the value of $k$ Also, find the co-ordinates of point $Q.$
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