Question

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”

1. the equation that explains the relationship between BC and B”C” is:
BC = 2 * B”C”
This equation states that the length of BC is equal to twice the length of B”C”.
Step-by-step explanation:
If 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, then the coordinates of the vertices of triangle A”B”C” can be expressed as follows:
A” (x+1, y+1)
B” (3x+3, 3y+3)
C” (3x+6, 3y+6)
To find the equation that explains the relationship between BC and B”C”, we can use the distance formula to find the length of both segments. The distance formula is:
distance = √((x2 – x1)^2 + (y2 – y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the distance formula, we can find the length of BC as follows:
BC = √((3x – x)^2 + (3y – y)^2)
= √((2x)^2 + (2y)^2)
= √(4x^2 + 4y^2)
= 2√(x^2 + y^2)
We can also find the length of B”C” as follows:
B”C” = √((3x+6 – 3x-3)^2 + (3y+6 – 3y-3)^2)
= √((3)^2 + (3)^2)
= √(9 + 9)
= √(18)
= 3√(2)