Question

Connor is constructing square ABCD. He has plotted A at (−2, 4), C at (−1, 1) and D at (−3, 2). Which coordinate could be the location of point B?

B (0, 3)
B (0, 0)
B (1, 1)
B (−1, 2)

Answer 1

The correct answer is B (0, 3).

Explanation:

A square has all sides of equal length and all angles equal to 90 degrees.

First, let's calculate the distance between points A and C, which will be the side length of the square. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula √[(x2-x1)² + (y2-y1)²].

For points A(-2, 4) and C(-1, 1), the distance AC is √[(-1 - -2)² + (1 - 4)²] = √[1² + -3²] = √[1 + 9] = √10.

Now, we need to find a point B such that the distance from B to C is also √10 and the angle ACB is 90 degrees.

Let's calculate the distance from each option to point C:

1. B(0, 3): BC = √[(0 - -1)² + (3 - 1)²] = √[1² + 2²] = √5.

2. B(0, 0): BC = √[(0 - -1)² + (0 - 1)²] = √[1² + -1²] = √2.

3. B(1, 1): BC = √[(1 - -1)² + (1 - 1)²] = √[2² + 0²] = √4 = 2.

4. B(-1, 2): BC = √[(-1 - -1)² + (2 - 1)²] = √[0² + 1²] = 1.

None of these distances are √10, so none of these points can be B.

However, if we consider that the square could be rotated, we can calculate the distance from point D to each option:

1. B(0, 3): DB = √[(0 - -3)² + (3 - 2)²] = √[3² + 1²] = √10.

So, if we consider a rotated square, point B could be at (0, 3).