Question

Given the information below find the coordinates for y

Answer 1

Option A. Y(15,0)

Explanation:

A=(1,0)=(xa,ya)→xa=1, ya=0

B=(5,0)=(xb,yb)→xb=5, yb=0

C=(2,3)=(xc,yc)→xc=2, yc=3

X=(7,0)=(xx,yx)→xx=7, yx=0

Z=(9,6)=(xz,yz)→xz=9, yz=6

We can see that the point C=(2,3) is transformed to point Z=(9,6)

There is a dilation from ABC to XYZ:

Factor of dilation: f=yz/yc=6/3→f=2

f*xc=2*2=4 different to xz=9, then, there is a translation too to the right:

xz-xc=9-4=5 units

Then, the transformation is a dilation with a factor of 2 and a horizontal translation to the right of 5 units, let's check it:

xz=f*xc+5=2*2+5=4+5→xz=9 ok

yz=f*yc=2*3→yz=6 ok

xx=f*xa+5=2*1+5=2+5→xx=7 ok

yx=f*ya=2*0→yx=0 ok

Then:

xy=f*xb+5=2*5+5=10+5→xy=15

yy=f*yb=2*0→yy=0

Y=(xy,yy)→Y=(15,0)

Answer 2

Option A (15,0) is the correct answer.

Explanation:

It is given that,

ΔABC ~ ΔXYZ

Therefore their sides are in same ratio.

And AB~XY, BC~YZ and AC~XY

or, AB/XY = BC/YZ and AC/XY

To find AB, BC and AC

It is given that, A(1,0), B(5,0),C(2,3),X(7,0)and Z (9,6)

By using distance formula,

AB = 4

BC = 3√3

AC =√10

To find XZ

XZ = √40 = 2√10

AC ~ XZ

AC/XZ = 1/2

To find coordinates of Y

AB ~ XY and AB/XY = 1/2

XY = 2AB = 2 * 4 = 8

Substituting the options

Option A) Y (15,0)

X(7,0)

XY = 8

Therefore AB/XY = 4/8 = 1/2

Therefore option A is the correct answer.