Show that the points(a,b),(a-+3,b+4),(a-1,b+7) and (a-4,b+3) are the vertices of a parallelogram.

Asked by hajerianvi2002 | 19th Feb, 2018, 11:38: PM

Expert Answer:

begin mathsize 16px style Let space straight P left parenthesis straight a comma straight b right parenthesis comma space straight Q left parenthesis straight a plus 3 comma straight b plus 4 right parenthesis comma space straight R left parenthesis straight a minus 1 comma straight b plus 7 right parenthesis comma space straight S left parenthesis straight a minus 4 comma straight b plus 3 right parenthesis
Slope space of space PQ equals fraction numerator straight b plus 4 minus straight b over denominator straight a plus 3 minus straight a end fraction equals 4 over 3
Similarly space find space slope space of space QR comma space RS comma space PS
Slope space of space QR equals fraction numerator negative 3 over denominator 4 end fraction
Slope space of space RS equals 4 over 3
Slope space of space PS equals fraction numerator negative 3 over denominator 4 end fraction
Hence comma space slope space of space PQ equals slope space of space RS
Slope space of space QR equals Slope space of space PS
Hence comma space PQRS space is space straight a space parallelogram. end style

Answered by Sneha shidid | 20th Feb, 2018, 09:27: AM