Answer

Verified

427.8k+ views

**Hint:**We will first draw a rectangle with the help of given three coordinates on the graph. Examining the graph, we will find the fourth coordinate. Similarly, we will find the midpoint of CD using a graph or midpoint formula. At last to calculate the area of the rectangle we will require length and breadth of rectangle because area of rectangle = length x breadth. We will find length and breadth using distance formulas between coordinates. Distance between two points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is given by \[\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}\].

**Complete step-by-step solution**Let us draw a graph using three coordinates and drawing perpendicular lines to find coordinates of D.

As from the graph, we can see that coordinates of D are $\left( 4,-1 \right)$. Now let us use the midpoint formula to find the midpoint of CD.

Coordinates of C are $\left( 4,7 \right)$ and coordinates of D are $\left( 4,-1 \right)$.

Midpoint of CD is given by

$\begin{align}

& \left( \dfrac{4+4}{2},\dfrac{7-1}{2} \right) \\

& =\left( \dfrac{8}{2},\dfrac{6}{2} \right) \\

& =\left( 4,3 \right) \\

\end{align}$

Hence, the midpoint of CD is $\left( 4,3 \right)$.

Now, we have to calculate the area of the rectangle. For that, we have to find the length and breadth which is given by distances between AB and BC.

Using distance formula on AB, we get –

$\begin{align}

& AB=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}} \\

& =\sqrt{{{\left( 2-2 \right)}^{2}}+{{\left( 7-\left( -1 \right) \right)}^{2}}} \\

& =\sqrt{{{\left( 8 \right)}^{2}}} \\

& =8 \\

\end{align}$

Using distance formula on BC, we get –

$\begin{align}

& AB=\sqrt{{{\left( 4-2 \right)}^{2}}+{{\left( 7-7 \right)}^{2}}} \\

& =\sqrt{{{\left( 2 \right)}^{2}}} \\

& =2 \\

\end{align}$

Hence, length $=8units$ and breadth $=2units$.

The area of the rectangle is given by length x breadth. Therefore,

Area of rectangle $=8\times 2=16~square~units$.

**Note:**Students should carefully mark points on graphs. Lines must be perpendicular to obtain an accurate value of point D. Students can also check coordinates of D by measuring the distance between CD and AB and checking them if they are equal. The midpoint of the CD can also be found with the help of the graph. It is important to mark the X and Y-axis on the graph. To find midpoint through the graph, draw diagonals and then draw lines from the center to CD to obtain the point on CD.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

How do you graph the function fx 4x class 9 maths CBSE