The coordinates of ▭WISH are given. Plot and connect the following set of points in the Cartesian Plane. Decide whether WISH is a rectangle, rhombus or a square.

Question

(a) W (-4, 0); I (3, 7); S(6, 4); H(-1, -3)

(b) W (1, 1); I (-2, 4); S(-5, 1); H(-2, -2)

Answer 1

a) W(-4,0) I(3,7) S(6,4) H(-1,-3)

WI has slope = 7/7 = 1, and length = 7sqr2

IS has slope = 3/-3 =-1 and length = 3sqr2

SH has slope = 7/7 = 1 and length 7sqr2 = slope and length of WI

WH has slope = 3/-3 = -1 and length 3sqr2 = slope and length of IS

the angles are 90 degrees, perpendicular, slope 1 = 45 degrees = tan^-1(1)

slope -1 is -45 degrees

45 - - 45 = 90 degrees. all 4 angles of the parallelogram are 90 degrees

it's a rectangle

all 4 sides are not equal, so it's not a square

rhombus means opposite angles are equal, but 2 are acute and 2 are obtuse

WISH has all 4 angles = 90 degrees, = perpendicular angles, none are acute or obtuse

b) W(1,1), I(-2,4) S(-5,1) H(-2,-2)

WI has slope = 3/-3 = -1 and length = 3sqr2

IS has slope = 3/3 = 1 and length = 3sqr2

SH has slope = 3/-3 = -1 and length = 3sqr2

WH has slope = 3/3 = 1 and length = 3sqr2

all lengths are equal

all angles are perpendicular

it's a square

not a rhombus, no acute or obtuse angles

a square is a rectangle though, a special type of rectangle

so the quadrilateral is both a square and a rectangle, but square is the "better" answer

but "best" answer is both a square and a rectangle