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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"

User Sshine
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15 votes
15 votes

Answer:

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".

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)

User Tomas Lukac
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