Find the coordinates of the other two vertices, Mathematics

Assignment Help:

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.                                                                                                                                           (Ans: (1, 0), (1, 4))

Ans :  AB = BC ⇒ AD2 = BC2

(x + 1)2 + (y-2)2 = (x-3)2 + (y-2)2

x2 + 2x + 1 + y2 - 4y + 4 = x2 - 6x + 9 + y2 - 4y + 4

2x - 4y + 5 = - 6x - 4y + 13

8x = 13 - 5      8x =     8  ⇒   x = 1

On substituting in (x-3)2 + (y-2)2 + (x+1)2 + (y-2)2

= (-1 -3)2 + (2 - 2)2

We get y = 4 or 0.

∴B (1, 4) or (1, 0)

AD = DC ⇒ AD2 = DC2

(x1 + 1)2 + (y1-2)2 = (x1-3)2 + (y1-2)2

∴ x = 1.

On substituting in (x1 + 1)2 + (y1-2)2 + (x1-3)2 + (y1-2)2 = 16

We get y1 = 0 or 4.

∴ D (1, 4) or (1, 0)

∴the opposite vertices are (1, 4) & (1, 0)


Related Discussions:- Find the coordinates of the other two vertices

Introduction To Numerical Methods & Matlab, Can you help me with the course...

Can you help me with the coursework i have in Matlab?

Application of statistics-forecasting, Forecasting Statistics is very ...

Forecasting Statistics is very significant for business managers while predicting the future of a business for illustration if a given business situation includes a independen

Toni tiger, Application Practice Answer the following questions. Use Equat...

Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Sav

Area, area of r=asin3x

area of r=asin3x

Graph f(x) = ex and g(x) = e- x - common graph, Graph f ( x ) = e x and g ...

Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd