Question

quadrilateral abc is graphed on a coordinate plane. vertex a is located at the point (-2,3) . the quadrilateral is dilated by a scale factor of 2 , with the center of dilation at the origin, to form quadrilateral abcd. which ordered pair represents the location of vertex a? (-4, 5) (-4, 6) (0, 5) (6,-4)

Explanation:

Step1: Recall Dilation Formula

When a point \((x,y)\) is dilated with a scale factor \(k\) centered at the origin, the new point \((x',y')\) is given by \(x' = k \times x\) and \(y' = k \times y\).

Step2: Apply Dilation to Point A

Given point \(A(-2,3)\) and scale factor \(k = 2\). Calculate \(x'\) and \(y'\):
\(x' = 2\times(-2)= - 4\)
\(y' = 2\times3 = 6\)
So the coordinates of \(A'\) are \((-4,6)\).

Answer:

B. \((-4, 6)\) (assuming the second option is labeled B, as per the options given: first \((-4,5)\), second \((-4,6)\), third \((0,5)\), fourth \((6,-4)\))