Triangle A"B"C" is formed using the translation (x+1, y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship between BC and B"C"?

(Option b): segment BC = segment B double prime C double prime over 3

A complete question related to this found at (ID: 13432500) is stated below:

Triangle A″B″C″ is formed using the translation (x + 1, y + 1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship between segment BC and segment B double prime C double prime? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3

a) segment B double prime C double prime = segment BC over 3

b) segment BC = segment B double prime C double prime over 3

c) segment B double prime C double prime over segment BC = one third

d) segment BC over segment B double prime C double prime = 3

Step-by-step explanation:

Scale factor = 3

∆ABC = original image

∆ABC was dilated to get ∆A"B"C"

∆A"B"C" = new image

DO(x,y) →3(x,y)

To determine which equation explains the relationship between segment BC and segment B"C", first we would find the distance B and C.

Coordinates of ∆ABC

A =(-3, 3)

B= (1, -3)

C= (-3, -3)

The distance B and C = length of Segment BC

the distance between two points = √[(∆x)² + (∆y)²]

= √[(-3-(-3))² + (-3-1)²] = √[(-3+3)² + (-3-1)²]

= √(0+16) = √16 = 4

Length of Segment BC = 4 units

Length of Segment B"C" = scale factor × Length of Segment BC

B"C" = 3 × BC = 3(4) = 12

Since what we need is the equation of the relationship between the segments

B"C" = 3 × BC

BC = B"C"/3

(Option b): segment BC = segment B double prime C double prime over 3