00:01
Hello everyone, in this question we have been given a triangle in which the coordinate of point a is minus 9 minus 8 and that of c is minus 5 minus 6 and of point e is 3 minus 2 and the triangle is shown in the figure so here the triangle is so in the first part of the question we have to find the scale factor so for that we will find the length of side ac so by using the distance formula that is x2 minus x1 whole squared plus y2 minus y only square and this is under the square root so for ac we can write square root of minus 9 minus minus 5 only squared plus minus 8 minus minus minus minus 6 whole square so if we solve this we will get ac is equal to 16 plus 4 so this is equal to 2 square root of 5 and similarly we can find the length a e equal to square root of 3 minus minus 9 whole square plus minus 2 minus 8 whole square so again if we start this we will get square root of 144 plus 36 that is we can write this as 6 square root of 5 now we can write scale factor that is k equal to ae divided by ac so ae is 6 is square root of 5 and ac is 2 square root of 5 so if we solve this we will get 3 so therefore we can write scale factor k is equal to 3 for the second part that is center of dilation.
02:31
Let us consider the coordinate of center is x0 and y not.
02:35
Then x0 is equal to k times x1 minus x2 divided by k minus 1.
02:47
Similarly, y not equal to k times y1 minus y2 divided by k minus 1.
02:56
So for that we will need to find x1 and x2.
03:00
In triangle, a, b, c, the coordinate of a is minus 9 and minus 8.
03:11
And suppose this is x1 and y1.
03:16
Similarly, in triangle, a, c, coordinate a is equal to also minus 9.
03:25
Since both are common points in the triangles, so we will consider this as x2, y2.
03:32
Now if we put the value in the formula, we will get x0 is equal to...