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A has coordinates (1, 4)
B has coordinates (3,0)
C has coordinates (-3,-2)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.

Sagot :

Nepalieducation

Answer:

Step-by-step explanation:

Solution,

For the midpoint of AB

[tex]x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\x=\frac{1+3}{2} ,y=\frac{4+0}{2} \\\\x=2,y=2[/tex]

Hence, co-ordinate of D is D(2,2)

For the midpoint of AC

[tex]x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\x=\frac{1-3}{2} ,y=\frac{4-2}{2} \\\\x=-1,y=2[/tex]

Hence coordinate of E is E(-1,2)

Now find the slope of DE and BC if they are equal they are parallel

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