**Distance and area in the coordinate plane :**

We can solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

We can use coordinates to find the area of a figure and and absolute value to find distances between points with the same first coordinate or the same second coordinate.

**Example 1 :**

Find the distance between points A and B in the graph given below.

**Solution :**

From the graph, the ordered pair of A is (3, 3) and B is (3, -4)

Since, the distance is parallel to "y" axis, let us take the "y" coordinates in the two points A and B.

They are 3 and -4.

To find the distance between the two points , we have to add the absolute values of the y-coordinates

Then, the distance between the two points A and B is

= |3| + |-4|

= 3 + 4

= 7

Hence, the distance between points A and B is 7 units.

**Example 2 :**

Find the distance between points A and B in the graph given below.

**Solution :**

From the graph, the ordered pair of A is (3, 3) and B is (-4, 3)

Since, the distance is parallel to "x" axis, let us take the "x" coordinates in the two points A and B.

They are 3 and -4.

To find the distance between the two points , we have to add the absolute values of the x-coordinates

Then, the distance between the two points A and B is

= |3| + |-4|

= 3 + 4

= 7

Hence, the distance between points A and B is 7 units.

**Example 2 :**

What type of polygon can you make by plotting these points ?

Point A (-4, 2)

Point B (2, 2)

Point C (-4, -2)

Point D (2, -2)

And also find the area of the polygon made by these points.

**Solution : **

To know the type of the polygon, let us plot the given points on the coordinate plane.

When we plot the given points on the coordinate plane, it is clear that **the polygon we get is rectangle**.

Here, AB represents the length and AC represents the width of the rectangle ABCD.

To find the area of the rectangle, we have to find the length AB and width AC.

**Finding the length AB : **

From the graph, the ordered pair of A is (-4, 2) and B is (2, 2)

Since, the distance is parallel to "x" axis, let us take the "x" coordinates in the two points A and B.

They are -4 and 2.

To find the distance between the two points , we have to add the absolute values of the x-coordinates

Then, the distance between the two points A and B is

= |-4| + |2|

= 4 + 2

= 6

Therefore, the length AB is 6 units.

**Finding the width AC :**

From the graph, the ordered pair of A is (-4, 2) and B is (-4, -2)

Since, the distance is parallel to "y" axis, let us take the "y" coordinates in the two points A and B.

They are 2 and -2.

To find the distance between the two points , we have to add the absolute values of the y-coordinates

Then, the distance between the two points A and B is

= |2| + |-2|

= 2 + 2

= 4

Therefore, the width AB is 4 units.

**Finding area of the rectangle ABCD : **

Area of the rectangle ABCD is

= length x width

= 6 x 4

= 24

Hence, the area of the rectangle ABCD is 24 square units.

After having gone through the stuff given above, we hope that the students would have understood "Distance and area in the coordinate plane".

Apart from the stuff "Distance and area in the coordinate plane", if you want to know more about "History of statistics", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**