Question

1. Consder the following graph. 20 TE 18 14 12 14 1 1 2 13 -10 12 -14 15 I - 1 Part A: Under a diation of scale factor1/2 centered at (7,5), SM becomes HG. Determine the coordinates of HG and sketch HG on the graph. Part B: Under o dilation of scale factor 2 centered at the origin, SM becomes TP. Determine the coordinates of TP and sketch TP on the graph, Part C: Under a dilation of scale factor 1/2centered at(-4,-6). SM becomes CB. Determine the coordinates of CB and sketch on the graph.

Answer 1

The coordinates of HG are (2.5,-1.5) , (1.5 , -1.5)

The first thing to do here is to note the points on the end-points of line SM

This is obtainable from the graph

The points are S and M

The coordinates of point S are (-2,-8) while the coordinates of point M are (-4,-6)

We now proceed from here to dilate these points so as to get HG with the dilation centered at point (7,5)

Mathematically, to dilate a point F (x,y) , using a scale factor k centered at point (a,b)

We get the coordinates of the new point after the dilation as;

F' = (k(a-x) + x , k(b-y) + y)

With respect to this question, scale factor K is 1/2 while (a,b) is (7,5)

Thus, the coordinates of point H obtainable from point S (-2,-8) will be;

H = (1/2(7-(-2) - 2, 1/2(5-(-8) -8)

H = (1/2(9) - 2 , 1/2(13) - 8)

H = (4.5-2 , 6.5-8)

The coordinates of point H is (2.5 , -1.5)

We now proceed to get the coordinates of point G

This is obtainable from point M (-4,-6)

Thus, we have

G = (1/2(7-(-4) - 4 , 1/2(5-(-6) - 6)

G = (1/2(11) - 4 , 1/2 (11) - 6)

G = (5.5-4 , 5.5-6)

G = (1.5 , -1.5)

So the coordinates of HG are (2.5,-1.5) , (1.5 , -1.5)

To sketch this on the graph, we simply locate the coordinates of the points H and G and join together