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astra-53 [7]
4 years ago
13

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 ve

rtex is
Mathematics
1 answer:
Sholpan [36]4 years ago
7 0

Answer: (-1, 1)

<u>Step-by-step explanation:</u>

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


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