Question

Abcd is a square . If a and c coordinate are (5,4) and (-1,6) respectively ?.find the coordinate of B and D

Answer 1

Answer:

B=(1,2)

D=(3,8)

Step-by-step explanation:

The midpoint of this square is given by;

$m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\\\m=(\frac{5+-1}{2},\frac{4+6}{2} )\\ \\m=(2,5)$

The vector from the midpoint to the vertex (5,4) is given as;

$(5-2,4-5)\\(3,-1)$

this is known as the direction vector.

From the midpoint we use the direction vector to get back to our two end points

$(5,4)=(2,5)+(3,-1)\\\\(-1,6)=(2,5)-(3,-1)$

The perpendicular direction vector comes from swapping the coordinates and negating one, therefore the other vertices of our square are;

$(2,5)+(-1,-3)=(1,2)\\\\(2,5)-(-1,-3)=(3,8)$

B=(1,2)

D=(3,8)