Question

co-ordinate geometry (plzz do 11 and 12)

Answer 1

11. we must show that the 3 points are equidistant.
A(2,2)
B(-2,-2)
C(-2√3,2√3)
using distance formula,
AB = √[(x1-x2)²+(y1-y2)²]
= √[(2+2)²+(2+2)²]
= √32 units
BC = √[(-2+2√3)²+(-2-2√3)²]
= √[16-8√3+16+8√3]
= √32 units
CA = √[(-2√3-2)²+(2√3-2)²]
= [16+8√3+16-8√3]
= √32 units
therefore AB = BC = CA = √32 units
therefore ABC is an equilateral triangle

12. we must show that opposite sides are equal.
A(-7,12)
B(19,18)
C(15,-6)
D(-11,-12)
using distance formula,
AB = √[(-7-19)²+(12-18)²]
= √[676+36] = √712 units
CD = √[(15+11)²+(-6+12)²]
= √[(676+36] = √712 units
BC = √[(19-15)²+(18+6)²]
= √[16+576] = √592 units
DA = √[(-11+7)²+(-12-12)²]
= √[16+576] = √592 units
therefore opposite sides of ABCD are equal: AB = CD, BC = DA
therefore ABCD is a parallelogram