If M (2,1) is the midpoint of PQ, then the equation of this line is

If M (2,1) is the midpoint of PQ, then the equation of this line is

P(a,0),Q(0,b)
M is the midpoint of the segment PQ
(a+0)/2=2,a=4
(0+b)/2=1,b=2
x/4+y/2=1
x+2y-4=0

If the symmetric point of point P (3, - 2) about X axis is point Q, then the length of segment PQ is?

For X-axis symmetry, the abscissa is constant and the ordinate is opposite to each other, so Q (3,2) then PQ = 4

As shown in the figure, fold the vertex a of a square paper ABCD with side length of 12 to the point E on the side so that de = 5 and the crease is PQ, then the ratio of PM and MQ is

∫△ amp ∫ ade, and AE = 13
∴AM＝13/2 ,AM/AD＝PM/DE＝13/24
PM＝DE*13/24＝65/24
Make BF ‖ PQ and hand it to F,
In △ ABF and △ ade
∠AFB=∠APQ=∠AED
∠FAB=∠ADE
AD=AB=12
∴△ABF≌△ADE
∴FB＝PQ＝AE＝13
MQ＝PQ-PM＝247/24
∴PM/MQ＝65/247

As shown in the figure, it is known that the shadow length MQ of the flagpole PQ on the ground is 22 meters. At this time, the angle between the light and the horizontal line is 52 degrees

tg52=PQ/MQ
PQ = tg52 * MQ tg52 = 1.2799, about 1.28
PQ = 1.28 * 22 = 28.16m