Given that point a (1,3) is on the image of the function y = K (x > 0), the edge BC of rectangle ABCD is on the x-axis, and E is the midpoint of diagonal BD, The image of function y = K (x > 0) passes through two points a and E, and the abscissa of point E is m (1) Find the value of K (2) find the abscissa of point C (expressed by M) (3) when ∠ abd = 45 °, find the value of M It is required to have steps to solve the problem and clear thinking

Given that point a (1,3) is on the image of the function y = K (x > 0), the edge BC of rectangle ABCD is on the x-axis, and E is the midpoint of diagonal BD, The image of function y = K (x > 0) passes through two points a and E, and the abscissa of point E is m (1) Find the value of K (2) find the abscissa of point C (expressed by M) (3) when ∠ abd = 45 °, find the value of M It is required to have steps to solve the problem and clear thinking

(1) Point a (1,3) on the image of y = K / X
Then 3 = K / 1, so k = 3
(2) This problem can be obtained by drawing
Because e (m, 1.5), ad = 2m-2
So the abscissa of C (2m-1,0) is 2m-1
(3) At this time, the rectangle is square ad = ab
2m-2=3
m=2.5