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Activity 9
Distance between two points and middle point of a segment of line.
1. In class locate two points in the Cartesian coordinate plane withthe condition that the abscissas and ordinates be different per both points and do the following: (2,3)(4,5)
a) Draw a line that passes by the firstpoint and is parallel to the X axis.
b) Draw a line that passes by the second point and is parallel to the Y axis.
c) Determine theintersection point of both lines and called it as point M.
d) What polygon is formed with the segments of line P1M MP2 and P1P2?
A triangle.
e) What isthe length of the segment of line P1M?
P1M= X2-X1
P1M=(4)-(2)
P1M=2
f) What is the length of the segment of line MP2?
MP2=Y2-Y1
MP2=(5)-(3)MP2=2
g) Then, with these last two values, how do you determine the length of the segment of line P1P2? Is this value the distance between the twopoints P1 and P2?
D=√(X2-X1)2+(Y2-Y1)2
D=√(4-2)2+(5-3)2
D=√22+22
D=√4+4
D=√8
D=2.8

M
M

2. Based on the following figure, answerthe questions and determine the formula to calculate the distance between the two points P(x1,y1) P(x2,x2).(3,5)(2,7)
a) What is the length of thesegment of line P1M?
p1M=x2-x1=2-3=-1
b) what is the length of the segment of line MP2?
Y2-y1=7-5=2
c) do you remember which is the theorem used todetermine the length of a side of a right triangle if it is know the length of the other two sides’ explain it.
Yes, is the Pythagorean theorem.