Question

Compress the triangle with vertices A (0, 0), B (1, 5), and C (5, 1) to one-third of its
size while keeping C (5, 1) fixed.

Answer 1

Answer:

hope it's help to you

Explanation:

If we want to magnify the triangle abc to

twice its size keeping c(5,2) fixed, we need to execute the following steps: Step 1: First, we need to translate the triangle by T_(-5,-2) so that point c(5,2) become

c(0,0).

Step 2: Then make its size twice using the scale factor of 2.

Step 3: After following the above steps, we need to translate the triangle back i.e. translate the triangle by T_(5,2).

=> T_(a,b) moves all the points by a unit in x-direction and b unit in the y-direction.

So, translating the triangle by T_(-5,-2)

a(0,0) -> a(0-5,0-2)= a(-5,-2)

b(1,1)> b(1-5,1-2)= b(-4,-1)

c(5,2)-> c(5-5,2-2)= c(0,0)

Now, magnifying the its size twice with scale factor of 2,

a(-5,-2) -> a(-5*2,-2*2)= a(-10,-4) b(-4,-1) -> b(-4*2,-1*2)= b(-8,-2)

c(0,0) -> c(0*2,0*2)= c(0,0)

Executing the last step, we get: a(-10,-4) -> a(-10+5,-4+2)= a(-5,-2) b(-8,-2) -> b(-8+5,-2+2)= (-3,0) c(0,0) -> c(0+5,0+2)= c(5,2)