The Mid-Point of a Line Segment

The points $A(-5,4), B(-1,-2)$ and $C(5,2)$ are the vertices of an isosceles right -angled triangle where the right angle is at $B$. Find the coordinates of $D$ so that $ABCD$ is a square.

If the mid-point $(x,y)$ of the line joining $(3,4)$ and $(p,7)$ lies on $2x+2y+1=0$, then what will be the value of $p$?

The centre of a circle is $(-4,2)$. If one end of the diameter of the circle is $(-3,7)$ then find the other end.

Find the midpoints of the line segment joining the points $\left(\frac{1}{2},-\frac{3}{7}\right) \mathrm{and} \left(\frac{3}{2},\frac{-11}{7}\right)$.

Find the midpoints of the line segment joining the points $(a,b) \mathrm{and} (a+2b,2a-b)$.

Find the midpoints of the line segment joining the points $(8,-2) \mathrm{and} (-8,0)$.

Find the midpoints of the line segment joining the points $(-2,3) \mathrm{and} (-6,-5)$.

If $D$ is the midpoint of $AC$ and $C$ is the mid-point of $AB$, then find the length of $AB$ when $AD=4 \mathrm{cm}$.

If $\left(a_1,b_1\right),\left(a_2,b_2\right)$ and $\left(a_3,b_3\right)$ are the midpoints of the sides of a triangle, whose values are $\left(5,1\right),\left(3,-5\right),\left(-5,-1\right)$ respectively, then find the value of $\left(a_1+a_3-a_2,b_1+b_3-b_2\right),\left(a_1+a_2-a_3,b_1+b_2-b_3\right)$ and $\left(a_2+a_3-a_1,b_2+b_3-b_1\right).$ Compare the results. What do you observe? Give reason for your result?

$A(6,1), B(8,2)$ and $C\left(9,4\right)$ are three vertices of a parallelogram $ABCD$ taken in order. Find the fourth vertex $D$. If $\left(x_1,y_1\right),\left(x_2,y_2\right),\left(x_3,y_3\right)$ and $\left(x_4,y_4\right)$ are the four vertices of the parallelogram, then using the given points, find the value of $\left(x_1+x_3-x_2,y_1+y_3-y_2\right)$ and state the reason for your result.

If $\left(3,x\right)$ is the midpoint of the line segment joining the points $A(8,-5)$ and $B(-2,11)$, then find the value of $\text{'}x\text{'}$.

Let $X$ be the midpoint of the line segment joining $A(3,0)$ and $B(-5,4)$ and $Y$ be the midpoint of the line segment joining $P(-11,-8)$ and $Q(8,-2)$. Find the midpoint of the line segment $XY$.

The mid-point of the line joining $(-\mathrm{a}, 2\mathrm{b})$ and $(-3 \mathrm{a},-4\mathrm{b})$ is

If the coordinates of one end of a diameter of a circle is $(3,4)$and the coordinates of its center is $(-3,2),$ then the coordinate of the other end of the diameter is

If $P\left(\frac{a}{3},\frac{b}{2}\right)$ is the midpoint of the line segment joining $A(-4,3)$ and $B(-2,4)$ then $\left(a,b\right)$

$A(-3,2),B(3,2) \mathrm{and} C(-3,-2)$ are the vertices of the right triangle, right-angled at $A$. Show that the mid point of the hypotenuse is equidistant from the vertices.

The points $A(-5,4), B(-1,-2)$ and $C(5,2)$ are the vertices of an isosceles right-angled triangle at $\angle B$ as $90°$. Find the coordinates of $D$, so that $ABCD$ is a square.

$O(0,0)$ is the centre of a circle whose one chord is $AB$, where the points $A$ and $B$ are $(8,6)$ and $(10,0)$respectively. $OD$ is the perpendicular from the centre to the chord $AB$. Find the coordinates of the midpoint of $OD$.

The midpoint of the sides of a triangle are $(2,4),(-2,3)$ and $(5,2)$. Find the coordinates of the vertices of the triangle.