Set 1.4 Question 26 See attachment. Work out (a) through (d). [ATTACH=full]116[/ATTACH]

a) A=(1,1) B=(9,3) C=(3,5) the lenth of sides: AB=sqrt((9-1)^2+(3-1)^2)=sqrt(8^2+2^2)=2sqrt(17) AC=sqrt((3-1)^2+(5-1)^2)=sqrt(2^2+4^2)=2sqrt(5) BC=sqrt((3-9)^2+(5-3)^2)=sqrt((-6)^2+2^2)=2sqrt(10) perimeter=2sqrt(17)+2sqrt(5)+2sqrt(10) perimeter=2(sqrt(17)+sqrt(5)+sqrt(10)) approximately, perimeter=19.04 b) triangle formed by joining midpoints of the three sides A=(1,1) B=(9,3) C=(3,5) midpoint AB is ((1+9)/2,(1+3)/2)=(10/2,2)=(5,2)...... => A'=(5,2) midpoint AC is ((1+3)/2,(1+5)/2)=(2,3)..........................=> B'=(2,3) midpoint BC is ((9+3)/2,(3+5)/2)=(6,4)..........................=> C'=(6,4) the length of sides: A’B'=sqrt((2-5)^2+(3-2)^2)=3.16 A’C'=sqrt((6-5)^2+(4-2)^2)=2.24 B’C'=sqrt((6-2)^2+(4-3)^2)=4.12 perimeter=3.16+2.24+4.12 perimeter=9.52 c) ratio of the perimeter in part (a) to the perimeter in part (b) perimeter(a)/perimeter(b)=19.04/9.52=2 d) The Midsegment Theorem The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.