Given that the line segment AB = a, P is a point on AB, and AP = ((radical 5-1) / 2) * a, find the ratio of AP to Pb, AB to AP, and ask whether the four line segments AP, Pb, AB and AP are equal

Given that the line segment AB = a, P is a point on AB, and AP = ((radical 5-1) / 2) * a, find the ratio of AP to Pb, AB to AP, and ask whether the four line segments AP, Pb, AB and AP are equal

AB: Pb = 1, AB; AP = radical 5-1 / A

Given that the two ends a and B of the line segment AB with the length of 1 + radical (2) slide on the x-axis and y-axis respectively, and AP = radical (2) and 2PB, the equation of P LOCUS C is obtained

Let a (a, 0), B (0, b), P (x, y),
Because | ab | = 1 √ 2,
So | ab | ^ 2 = 3 2 √ 2,
That is, a ^ 2 B ^ 2 = 3 2 √ 2. (1)
And because the vector AP = √ 2 / 2 * Pb
So (x-a, y) = √ 2 / 2 * (0-x, B-Y),
That is, x-a = √ 2 / 2 * (- x), y = √ 2 / 2 * (B-Y),
The solution is a = (1 √ 2 / 2) x, B = (1 √ 2) y,
Substituting (1) to (1 √ 2 / 2) ^ 2 * x ^ 2 (1 √ 2) ^ 2 * y ^ 2 = 3 2 √ 2,
This is the trajectory equation of P

Point P divides line AB into two segments AP and Pb, and AP = 2 / 3-radical 5-1. Pb = 2 / 3-radical 5
A. AP = abxpb
B, Pb = abxap
C. AB = apxpb
D. None of the above is true

This is the golden ratio. The longer segment is the middle of the ratio between the shorter segment and the whole segment
The answer should be a
Method 2: let the length of the whole line segment be a
AP = (2 / 2 radical 5-1) a, Pb = (2 / 3 radical 5) a, ab = a
Then AP = abxpb
So the answer is a

Find the projection line equation of the line (x-1) / 1 = Y / 2 = Z / 3 on the plane 4x-y + Z-1 = 0

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It is known that in rectangle ABCD, ab = 3cm, ad = 9cm, fold the rectangle so that point B coincides with point D, and the crease is EF, then the area of △ Abe is______ A．6cm2B．8cm2   C．10cm2D．12cm2．

Fold the rectangle so that the point B coincides with the point D, ∵ be = ed. ∵ ad = 9cm = AE + de = AE + be. ∵ be = 9-ae, according to the Pythagorean theorem, AB2 + AE2 = be2. The area of AE = 4. ∵ Abe is 3 × 4 ∵ 2 = 6