Answer:
(Option b): segment BC = segment B double prime C double prime over 3
A complete question related to this found at brainly (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
