Question

ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x-y plane. The
equation of the straight line AD is x + y = 1. What is the equation of BC?
a. x + y = –1
b. x – y = –1
c. x + y = 1
d. None of these

Answer 1

ANSWER

The equation of BC is x+y= -1
AD is positive so BC is negative.

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Answer 2

Answer:

The equation of line BC, x+y=-1

A is correct option.

Step-by-step explanation:

ABCD is a rhombus with diagonals AC and BD intersecting at the origin on x-y plane.

Please see the attachment for figure.

In the given, ABCD is rhombus. Side AD and BC are opposite sides of rhombus.

Opposite sides of rhombus are parallel. AD || BC

If the equation of line AD, x+y=1

As we know the slope of parallel line is equal.

Equation of line BC, x+y=k

Intersection of diagonals AC and BD at original. Coordinate A and C should be equi-distance from origin because diagonals bisect each other.

Therefore, Coordinate C: (0,-1)  and Coordinate B: (-1,0)

Hence, The equation of line BC, x+y=-1