**How to find the missing coordinate in a parallelogram :**

To find the missing coordinate of a parallelogram, we use one of the following methods.

(i) Using slope

(ii) Using midpoint formula

(iii) Using section formula

In a parallelogram, the opposite sides are parallel.If two lines are parallel, then its slopes will be equal.

Let us consider the parallelogram ABCD,

Slope of AB = Slope of CD

Slope of BC = Slope of AD

In a parallelogram

Midpoint of AC = Midpoint of BD

The point of intersection of diagonals divides the diagonal in the same ratio.

For example, if the the common point of both diagonals is in the ratio l : m, then the value of l and m are equal.

Let us look into some example problems to understand the above concepts.

**Example 1 :**

If (7, 3), (6, 1), (8, 2) and (p, 4) are the vertices of a parallelogram taken in order, then find the value of p.

**Solution :**

Let the vertices of the parallelogram be A (7, 3), B(6, 1), C (8, 2) and D (p, 4)

We know that the diagonals of a parallelogram bisect each other. The midpoints of the diagonal AC and the diagonal BD coincide.

Midpoint of AC = Midpoint of BD

Midpoint = (x_{1} + x_{2})/2 , (y_{1} + y_{2})/2

A (7, 3) and C (8, 2)

= (7 + 8)/2 , (3 + 2)/2

= (15/2, 5/2) ---------(1)

B (6, 1) and D (p, 4)

= (6 + p)/2 , (1 + 4)/2

= (6 + p)/2 , 5/2 ---------(2)

(15/2, 5/2) = ((6 + p)/2 , 5/2)

Equating x-coordinates, we get

15/2 = (6 + P) / 2

15 = 6 + p

Subtract 6 on both sides,

15 - 6 = 6 + p - 6

9 = p

Hence the missing coordinate is 9.

**Example 2 :**

Using the concept of slope, find the missing coordinate (-2 , -1), (4 , 0), (a , 3) and (-3 , 2) taken in order form a parallelogram.

**Solution :**

Let the vertices of the parallelogram be A (-2 , -1), B (4 , 0), C (a , 3) and D (-3 , 2)

Slope of AB = Slope of CD

Slope = (y_{2}- y_{1}) / (x_{2}-x_{1})

Slope of AB :

A (-2 , -1), B (4 , 0)

m = (0 - (-1)) / (4 - (-2))

m = (0 + 1) / (4 + 2)

m = 1 / 6 ------(1)

Slope of CD :

C (a , 3) and D (-3 , 2)

m = (2 - 3) / (-3 - a)

m = - 1 / (-3 - a)

m = 1 / (3 + a) ------(2)

1/6 = 1/(3 + a)

3 + a = 6

Subtract 3 on both sides

3 + a - 3 = 6 - 3

a = 3

Hence the missing coordinate is 3.

After having gone through the stuff given above, we hope that the students would have understood "How to find the missing coordinate in a parallelogram".

If you want to know more about the stuff "How to find the missing coordinate in a parallelogram" 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.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**