Answered: Calculate the coordinates of K’, L’,…

Calculate the coordinates of K’, L’, M’, N’ resulting from the scaling of K(2,2), L(5,2), M(5,4), N(2,4) by (3,3) in relation to its center. Write the transformation matrix.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 34E

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Question

Calculate the coordinates of K’, L’, M’, N’ resulting from the scaling of K(2,2), L(5,2), M(5,4), N(2,4) by (3,3) in relation to its center. Write the transformation matrix.

Expert Solution

We will use Midpoint Formula :-

X= $\frac{x_{1} + x_{2}}{2}$

Y= $\frac{y_{1} + y_{2}}{2}$

where (X,Y) is the midpoint of points (x₁,y₁) & (x₂,y₂)

Now X Coordinates of K' is

3= $\frac{x + 2}{2}$

x= 4

Now Y Coordinates of K' is

3= $\frac{y + 2}{2}$

y=4

Hence required K'(4,4)

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