It is known that: as shown in the figure, in the rectangular coordinate system xoy, one side of RT △ OCD OC is on the X axis. ∠ C = 90 °, point D is in the first quadrant, OC = 3, DC = 4, and the image of the inverse scale function passes through the midpoint a of OD. (1) find the analytical formula of the inverse scale function; (2) if the image of the inverse scale function intersects with the other side of RT △ OCD DC at point B, find the analytical formula of the straight line of a and B

It is known that: as shown in the figure, in the rectangular coordinate system xoy, one side of RT △ OCD OC is on the X axis. ∠ C = 90 °, point D is in the first quadrant, OC = 3, DC = 4, and the image of the inverse scale function passes through the midpoint a of OD. (1) find the analytical formula of the inverse scale function; (2) if the image of the inverse scale function intersects with the other side of RT △ OCD DC at point B, find the analytical formula of the straight line of a and B

(1) Let a cross point a as AE ⊥ X-axis at E. ∵ ∠ OCD = 90 ° and ∥ AE ∥ CD. A as OD midpoint, OC = 3, DC = 4, ∥ AE is the median line of △ OCD, ∥ OE = EC = 12oc, ∥ a (1.5, 2); let y = KX, then k = 1.5 × 2 = 3, ∥ y = 3x; (2) when x = 3, y = 1, ∥ B (3, 1); let y = k2x + B, then 2 = 1.5k2 + B1 = 3k2 + B, the solution is obtained ：k2=-23b=3．∴y=-23x+3．

It is known that in the plane rectangular coordinate system xoy, one side OC of RT △ OCD is on the x-axis, ∠ C = 90 degrees
Point D is in the first quadrant, OC = 3, DC = 4. The image of the inverse scale function passes through the midpoint a (1) of OD to find the analytical formula of the inverse scale function. (2) if the image of the inverse scale function intersects with DC on the other side of RT △ OCD at B, find the linear analytical formula of a and B
Picture, you can imagine

(1) On one side of RT △ OCD, OC is on the x-axis, ∠ C = 90 °,
Point D is in the first quadrant, OC = 3, DC = 4,
So the coordinates of OD midpoint a are (3 / 2,2),
The analytic expression of inverse proportion function is y = 3 / X
(2) The inverse scale function intersects with DC on the other side of RT △ OCD at point B,
So the abscissa of B is 3, substituting y = 3 / x, the solution is y = 1, that is, the coordinate of point B is (3,1),
Let y = KX + B be the analytic expression of the line passing through two points a and B,
Substituting the coordinate values of a and B,
We obtain k = - 2 / 3, B = 3,
So the analytical formula of the straight line passing through a and B is y = - 2x / 3 + 3

In the plane rectangular coordinate system xoy, one side OC of the RT triangle OCD is on the x-axis, ∠ C = 90 ° and the point D is in the first quadrant. OC = 3, DC = 4, the graph of inverse scale function
(1) Find the analytic expression of the inverse proportion function.
(2) If the image of the inverse scale function intersects the DC on the other side of the RT triangle OCD at point B, then a is obtained. The analytic formula of the straight line of two points B.

(1) Point C (3,0) point d (3,4) you drop a sentence, that is, point a is the midpoint of OD, so point a coordinates (3 / 2,2) let the inverse scale function be y = K / x, and substitute it into a coordinates to get k = 3, so the inverse scale function y = 3 / X (2) point B coordinates (3, y) substitute it into y = 3 / x, y = 1 point B (3,1) AB slope = (2-1) / (3 / 2-3) = - 2 / 3A

As shown in Figure 1, in RT △ OCD, ∠ cod = 90 °, OC = OD, points a and B are on OC and OD respectively, ab ‖ DC. (1) please give the number of line segments AC and BD directly
As shown in Fig. 1, in RT △ OCD, ∠ cod = 90 °, OC = OD, points a and B are on OC and OD respectively, ab ‖ DC
(1) Please give the relationship between AC and BD directly
(2) Rotate △ OAB anticlockwise around point O, as shown in Figure 2, connecting AC and BD. is the conclusion in (1) still valid? If yes, please prove it; if not, please explain the reason;
(3) In Figure 2, connect AB, if OA = 1, ad = root 2, AC = 2, please find out the degree of ∠ Dao and the distance from point a to DC
Focus on the third question, find the distance between a and OC, and prove that this question will also be selected as a satisfactory answer, online, etc!

Solution (1) AC = BD
(2) If △ OAB in Figure 1 is rotated clockwise by an acute angle around point O, then AC is still equal to BD
∵ after rotating an angle at will, ∠ COA + ∠ AOD = 90 °, ∠ BOD + ∠ AOD = 90 °,
In addition, OC = OD, OA = ob,
∴△COA≌△DOB,∴AC=BD
(3) The third question is that I can't think of it without a picture. I feel that the distance of ∠ Dao = 90 ° is 2 / 2 of the root