Answer:
Option A (15,0) is the correct answer.
Step-by-step 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
<u>To find AB, BC and AC</u>
<u>It is given that, A(1,0), B(5,0),C(2,3),X(7,0)and Z (9,6)</u>
By using distance formula,
AB = 4
BC = 3√3
AC =√10
<u>To find XZ</u>
XZ = √40 = 2√10
AC ~ XZ
AC/XZ = 1/2
T<u>o find coordinates of Y</u>
AB ~ XY and AB/XY = 1/2
XY = 2AB = 2 * 4 = 8
<u>Substituting the options</u>
Option A) Y (15,0)
X(7,0)
XY = 8
Therefore AB/XY = 4/8 = 1/2
Therefore option A is the correct answer.