The vertices of a square are A(–2, 4), B(4, 4), C(4, –2), and D(–2, –2). The diagonals of the square intersect at their midpoint

Question

mote1985 [20]

3 years ago

5

The vertices of a square are A(–2, 4), B(4, 4), C(4, –2), and D(–2, –2). The diagonals of the square intersect at their midpoint

s.
What are the coordinates of the midpoint where the diagonals intersect?

(1, 1)
(–1, 4)
(2, 2)
(–3, 3)

Mathematics

1 answer:

sertanlavr [38] · Answer 1 · 2022-08-28T13:56:25+03:00

sertanlavr [38]3 years ago

4 0

A(–2, 4), B(4, 4), C(4, –2), D(–2, –2)
-> select some diagonal: AC
midpoint is at A+(1/2)*AC

-> calculate vector AC:
AC=(4-(-2),-2-4)=(6,-6)
-> calculate half length of AC:
(1/2)*AC=(3,-3)

A+(1/2)*AC=
(-2,4)+(3,-3)=(1,1) which is the midpoint

so the first option is correct