The points A(4, -1), B(6, 0), C(7, 2) and D(5, 1) are the vertices of a rhombus. Is ABCD also a square?

Asked by Topperlearning User | 26th Jul, 2017, 02:48: PM

Expert Answer:

T h e space g i v e n space p o i n t s space a r e space A left parenthesis 4 comma space minus 1 right parenthesis comma space B left parenthesis 6 comma space 0 right parenthesis comma space C left parenthesis 7 comma space 2 right parenthesis space a n d space D left parenthesis 5 comma space 1 right parenthesis.
U sin g space d i s tan c e space f o r m u l a comma
D i a g o n a l space A C equals square root of open parentheses 4 minus 7 close parentheses squared plus open parentheses negative 1 minus 2 close parentheses squared end root equals square root of 9 plus 9 end root equals square root of 18 space u n i t s
D i a g o n a l space B D equals square root of open parentheses 6 minus 5 close parentheses squared plus open parentheses 0 minus 1 close parentheses squared end root equals square root of 1 plus 1 end root equals square root of 2 space u n i t s
S i n c e comma space A C not equal to B D comma space A B C D space i s space n o t space a space s q u a r e.

Answered by  | 26th Jul, 2017, 04:48: PM