Example 4. As shown in the figure, in the plane rectangular coordinate system, there is a line segment AB, where a (6,9 / 2), B (6,0). (1) take the origin o as the quasi center, enlarge AB to 2 times, And the corresponding line CD is on the left side of the y-axis (2) Under the condition of (1), translate the position like center upward along the y-axis, and record it as P, so that the corresponding point D of a after translation is on the x-axis, then what is the length of OP? (3) What do you find in the calculation of 1 / AB + 1 / CD and 1 / op in question (2)? If the magnification of a and B coordinates are changed, is the conclusion still valid?

Example 4. As shown in the figure, in the plane rectangular coordinate system, there is a line segment AB, where a (6,9 / 2), B (6,0). (1) take the origin o as the quasi center, enlarge AB to 2 times, And the corresponding line CD is on the left side of the y-axis (2) Under the condition of (1), translate the position like center upward along the y-axis, and record it as P, so that the corresponding point D of a after translation is on the x-axis, then what is the length of OP? (3) What do you find in the calculation of 1 / AB + 1 / CD and 1 / op in question (2)? If the magnification of a and B coordinates are changed, is the conclusion still valid?

（1）C(-12,-9), D（-12,0）
(2) From the solution of point a (6,0) and point d (- 12,0), the analytic expression of straight line ad is y = 1 / 4x + 3,
∴OP=3
（3）1/AB+1/CD=1/3, 1/OP=1/3,
∴1/AB+1/CD=1/OP
If the magnification of a and B coordinates are changed, the conclusion is still valid

As shown in the figure, in the known plane rectangular coordinate system, a (- 1,3), B (2,1), line AB intersect Y axis at point C, and then calculate the coordinates of point C

When passing through point a as an ⊥ Y axis at point n, and passing through point B as BM ⊥ Y axis at point m, then ∠ ANC = ∠ BMC = 90 °, ∫ ACN = ∠ BCM, ∫ ANC ≁ BMC, ∫ anbm = NCMC, ∫ a (- 1,3), B (2,1), ∫ an = 1, OM = 1, BM = 2, NM = 2, ∫ 12 = NC2 − NC, the solution is: NC = 23, ∫ co = 3-23 = 73

As shown in the figure, in the rectangular coordinate system, the coordinates of two points a and B are (0, 3) and (4, 0), respectively. Then the coordinates of the midpoint P of the line AB are (0, 3) and (4, 0)______ ．

Let the line PD ‖ Ao intersect the x-axis at point E, let the line PE ‖ Bo intersect the y-axis at point D, ∵ OA ⊥ ob, PD ‖ OA, ∵ PD ⊥ ob, and ∵ p be the middle point of the line AB, ∵ d be the middle point of the edge OA, that is, OD = 12oa = 12 × 3 = 1.5. Similarly, the coordinates of OE = 12ob = 2 ⊥ P are (2,1.5)

If a (1, - 2) and B (3,0) are known in the plane rectangular coordinate system, then the coordinates of the midpoint of the line AB are ()
A. （2，-1）B. （2，1）C. （4，-2）D. （-1，2）

In the plane rectangular coordinate system, we know a (1, - 2), B (3, 0), and substitute the midpoint coordinate formula X & nbsp; = & nbsp; X1 + x22y & nbsp; = & nbsp; Y1 + Y22 to find out the coordinates of the midpoint of line AB as X = 2Y = - 1, so the coordinates of the midpoint of line AB are (2, - 1), so we choose a, B (3, 0) as the coordinates of the midpoint of line ab