**Vertices of rectangle question7 :**

Here we are going to see practice question on vertices of parallelogram.

**Definition of rectangle :**

A rectangle is a quadrilateral in which opposite sides are parallel and equal in length. In other words opposite sides of a quadrilateral are equal in length then the quadrilateral is called a rectangle.

(i) First we have to find the length of all sides using distance between two points formula.

(ii) The rectangle can be divided into two right triangles.

(iii) If the given four vertices satisfies those conditions we can say the given vertices forms a rectangle.

**Question 7 :**

Examine whether the given points P (0,-1) and Q (-2,3) and R (6,7) and S (8,3) forms a rectangle.

**Solution :**

To show that the given points forms a rectangle we need to find the distance between three points.

Distance Between Two Points (x ₁, y₁) and (x₂ , y₂)

**√(x₂ - x₁)² + (y₂ - y₁)²**

Four points are P (0,-1) and Q (-2,3) and R (6,7) and S (8,3)

Distance between the points P and Q

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 0, y₁ = -1, x₂ = -2 and y₂ = 3**

**= **
√(-2-0)² + (3-(-1))²

= ** **
√(-2)² + (3+1)²

= ** **
√4 + (4)²

= √4 + 16

= √20 units

Distance between the points Q and R

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = -2, y₁ = 3, x₂ = 6 and y₂ = 7**

**= **
√6-(-2))² + (7-3)²

= ** **
√(6+2)² + (4)²

= ** **
√8² + 16

= √64 + 16

= √80 units

Distance between the points R and S

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 6, y₁ = 7, x₂ = 8 and y₂ = 3**

**= **
√(8-6)² + (3-7)²

= ** **
√(2)² + (-4)²

= ** **
√4 + 16

= √20 units

Distance between the points S and P

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 8, y₁ = 3, x₂ = 0 and y₂ = -1**

**= **
√(0-8)² + (-1-3)²

= ** **
√(-8)² + (-4)²

= √64 + 16

= √80 units

PQ = √20 units

QR = √80 units

RS = √20 units

SP = √80 units

Length of opposite sides are equal.To test whether it forms right triangle we need to find the length of diagonal PR.

Distance between the points P and R

= **√(x₂ - x₁)² + (y₂ - y₁)²**

Here **x₁ = 0, y₁ = -1, x₂ = 6 and y₂ = 7**

**= **
√(6-0)² + (7-(-1))²

= ** **
√(6)² + (7+1)²

= ** **
√6² + 8²

= √36 + 64

= √100 units

PR² = PS² + SR²

(√100)² = (√80) ² + (√20)²

100 = 80 + 20

100 = 100

So the given vertices forms a rectangle.

(1) Examine whether the given points A (-3,2) and B (4,2) and C (4,-3) and D (-3,-3) forms a rectangle.

(2) Examine whether the given points A (8,3) and B (0,-1) and C (-2,3) and D (6,7) forms a rectangle.

(3) Examine whether the given points A (-2,7) and B (5,4) and C (-1,-10) and D (-8,-7) forms a rectangle.

(4) Examine whether the given points P (-3,0) and Q (1,-2) and R (5,6) and S (1,8) forms a rectangle.

(5) Examine whether the given points P (-1,1) and Q (0,0) and R (3,3) and S (2,4) forms a rectangle.

(6) Examine whether the given points P (5,4) and Q (7,4) and R (7,-3) and S (5,-3) forms a rectangle.

(7) Examine whether the given points P (0,-1) and Q (-2,3) and R (6,7) and S (8,3) forms a rectangle.

(8) Examine whether the given points A (2,-2) and B (8,4) and C (5,7) and D (-1,1) forms a rectangle.

- Solution for vertices of rectangle question1
- Solution for vertices of rectangle question2
- Solution for vertices of rectangle question3
- Solution for vertices of rectangle question4
- Solution for vertices of rectangle question5
- Solution for vertices of rectangle question6
- Solution for vertices of rectangle question7
- Solution for vertices of rectangle question8

After having gone through the stuff given above, we hope that the students would have understood "Vertices of rectangle question7".

Apart from the stuff given above, if you want to know more about "Vertices of rectangle question7", 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**