The perimeter of a rectangle changes from 2.5 to 10 after dilation what was the scale factor of the dilation
2 answers:
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Answer: The correct option is (D) (4, -6).
Step-by-step explanation: Given that the areas of the triangles ADC and DCB are in the ratio 3 : 4.
We are to find the co-ordinates of point C.
From the diagram, we note that
the co-ordinates of point A and B are A(1, -9) and B(8,-2).
So, the length of the line segment AB, calculated by distance formula, is
Now, area of ΔADC is
and area of ΔDCB is
According to the given information, we have
So, the point C divides the line segment AB internally in the ratio 3 : 4.
We know that
if a point divides a line segment with end-points (a, b) and (c, d) internally in the ration m : n, then its co-ordinates are
Since point C divides the line segment AB with end-points A(1, -9) and B(8, -2) internally, so the co-ordinates of point C will be
Thus, the co-ordinates of point C are (4, -6).
Option (D) is correct.
