Question

translate triangle abc by 3 units to the left and 5 units down. which of the following are the coordinates of new triangle abc? (1 point)
○ a(7,0), b(5,−4), c(10,−2)
○ a(1,0), b(−1,−4), c(4,−2)
○ a(1,10), b(−1,6), c(4,7)
○ a(−1,2), b(−3,−2), c(2,0)

Explanation:

Step1: Find original coordinates of B

From the graph, point B has coordinates \((2, 1)\).

Step2: Apply translation rules

To translate a point \((x, y)\) 3 units left, we subtract 3 from the x - coordinate (\(x'=x - 3\)), and to translate 5 units down, we subtract 5 from the y - coordinate (\(y'=y - 5\)).
For point B:
\(x'=2 - 3=-1\)
\(y'=1 - 5=-4\)
So the translated coordinates of B should be \((-1, - 4)\).
Now we check the options:

• First option: \(B'(5,-4)\) is incorrect.
• Second option: \(B'(-1,-4)\) matches our calculation. Let's verify the translation rule with a general point. If we assume the original coordinates of A and C follow the same translation (since it's a translation of the triangle), the second option's points are obtained by subtracting 3 from the x - coordinate and 5 from the y - coordinate of the original points (even if we don't know original A and C, the B point translation is a key indicator).
• Third option: \(B'(-1,6)\) is incorrect (we subtracted 5, not added).
• Fourth option: \(B'(-3,-2)\) is incorrect (calculation for y - coordinate is wrong).

Answer:

\(A'(1,0), B'(-1, - 4), C'(4,-2)\) (the second option)