Question

triangle abc has vertices a(1,2), b(4,3), and c(5,6). after translating this triangle 4 units down and then reflecting it across the x - axis, which are the coordinates of vertex a? (1, - 2) (1, - 6) (1,2) (1,6)

Explanation:

Step1: Translate vertex \(A\) 4 units down

When translating a point \((x,y)\) \(k\) units down, the new \(y\)-coordinate is \(y - k\). Here \(x = 1,y=2,k = 4\).
The new \(y\)-coordinate is \(2-4=-2\), so the point after translation is \((1,-2)\).

Step2: Reflect the translated point across the \(x\)-axis

When reflecting a point \((x,y)\) across the \(x\)-axis, the rule is \((x,y)\to(x,-y)\).
For the point \((1,-2)\), after reflection, the \(y\)-coordinate becomes \(-(-2)=2\).

Answer:

\((1,2)\)