Question

If the three vertices of a rectangle taken in order are the points (2, -2), (8, 4) and (5, 7). The co-ordinates of the fourth vertex is

Answer 1

Answer: (-1,1)

Explanation:

Answer 2

Answer: (-1, 1)

Explanation:

Let D represent the fourth vertex with coordinate (x, y)

Since ABCD is a rectangle, then BC || AD and AB || DC

Since BC is parallel to AD, then they have the same slope (m) = -1

Equation of line AD: y - (-2)) = -1(x - 2) ⇒ y + 2 = -x + 2 ⇒ y = -x

Since AB is parallel to DC, then they have the same slope (m) = 1

Equation of line DC: y - 7 = 1(x - 5) ⇒ y - 7 = x - 5 ⇒ y = x + 2

D is where the two lines intersect so the next step is to solve the system of equations: y = -x and y = x + 2

Using substitution method: -x = x + 2 ⇒ -2x = 2 ⇒ x = -1

Now solve for y: y = -x ⇒ y = -(-1) ⇒ y = 1

x = -1 and y = 1