Question

1. what are the new coordinates of the line segment ab after the triangle has been enlarged by a scale factor of 2? (2, 2) and (2, 10) (0, 2) and (10, 2) (2, 2) and (10, 2) (2, 2) and (7, 2)

Explanation:

Step1: Find original coordinates of A and B

From the graph, point A is at \((0, 2)\) and point B is at \((5, 2)\) (assuming each grid square is 1 unit, and A is on the y - axis at y = 2, x = 0; B is at x = 5, y = 2).

Step2: Apply scale factor of 2

To find the new coordinates after enlargement with a scale factor of \(k = 2\), we use the rule \((x,y)\to(kx,ky)\).
For point A \((0,2)\):
New \(x\) - coordinate: \(0\times2 = 0\)
New \(y\) - coordinate: \(2\times2=4\)? Wait, no, wait. Wait, maybe I misread the original coordinates. Wait, looking at the triangle, maybe A is \((0, 2)\) and B is \((5, 2)\), but when we enlarge by scale factor 2, the x - coordinate of B becomes \(5\times2 = 10\), and y - coordinate remains 2 (since it's a horizontal line segment AB, y - coordinate is constant). Wait, maybe the original A is \((0, 2)\) and B is \((5, 2)\). Then after scaling by 2, A becomes \((0\times2,2\times2)=(0,4)\)? No, the options have (0,2) and (10,2) as one of the options. Wait, maybe the original A is \((0, 2)\) and B is \((5, 2)\), and when we scale with respect to the origin? Wait, no, maybe the center of enlargement is the origin. Wait, let's re - examine. If the original coordinates of A are \((0, 2)\) and B are \((5, 2)\), then after multiplying each coordinate by 2 (scale factor 2), A becomes \((0\times2,2\times2)=(0,4)\)? But that's not in the options. Wait, maybe the original A is \((0, 2)\) and B is \((5, 2)\), but the scale factor is applied to the x - coordinate only? No, that doesn't make sense. Wait, the options include \((0,2)\) and \((10,2)\). So if we consider that the length of AB is 5 units (from x = 0 to x = 5 at y = 2), after scaling by 2, the length becomes \(5\times2 = 10\), so the new coordinates of A are \((0, 2)\) and B are \((10, 2)\) (if the y - coordinate remains the same, maybe the center of enlargement is on the line AB, so the y - coordinate doesn't change, and the x - coordinates are scaled by 2).

Answer:

(0, 2) and (10, 2) (the option with (0, 2) and (10, 2))