A (- 2, 2), B(8, 2) and C(4, - 4) are the vertices of a parallelo… - Vidyadip

Question

$A (- 2, 2), B(8, 2)$ and $C(4, - 4)$ are the vertices of a parallelogram $\text{ABCD}$. By plotting the given points on a graph paper; find the co$-$ordinates of the fourth vertex $D$.Also, form the sazmegraph,state the co$-$ordinates of the mid$-$points of the sides $AB$ and $CD.$

✓

Answer

Plot the points $A, B,$ and $C$ on the graph paper. Join the points to complete the parallelogram $\text{ABCD}$.
As the distance between points $A$ and $B$ is $10$ units, distance between the corners of the opposite side $C$ and $D$ will also be $10$ units.

Hence, the fourth point $D = (- 6, - 4)$
Mid point of $AB$ will lie at $5$ units distance from $A$ and $B$ both which is $= (3, 2)$
Mid point of $CD$ will lie at $5$ units distance from $C$ and $D$ both which is$ = (-1, -4)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Co-ordinate Geometry→Co-ordinate Geometry — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

The following data have been arranged in ascending order. If their median is $63,$ find the value of $x.34, 37, 53, 55, x, x + 2, 77, 83, 89$ and $100.$

The ratio of two numbers is $\frac{2}{3}$. If $2$ is subtracted from the first and $8$ from the second, the ratio becomes the reciprocal of the oriainal ratio. Find the numbers.

Write the logarithmic equation for:$n =\sqrt{\frac{ M \cdot g }{ m \cdot l }}$

If $a+2 b+3 c=0$, show that $a^3+8 b^3+27 c^3=18 a b c.$
[Hint. $x+y+z=0 \quad \Rightarrow x^3+y^3+z^3=3 x y z$.]

In $\tan \theta = 1$, find the value of $5\cot^2\theta + \sin^2\theta - 1$.

In the following, find the co$-$ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:$5 x-(5-x)=\frac{1}{2}(3-x) ; 4-3 y=\frac{4+y}{3}$

Calculate the area of a right$-$angled triangle whose hypotenuse is $65\ cm$ and one side is $16\ cm$.

The measures of the angles of a quadrilateral are: $(2x - 4)^\circ , (5x - 10)^\circ , (4x - 8)^\circ $ and $(7x - 14)^\circ $. find $ x.$

Factorise the following:$(2p + q)^2 - 10p - 5q - 6$

Find the values of $x$ and $y$ if:$(5x - 3y, y - 3x) = (4, -4)$