Question

1. Plot two points to form a square in the above graph. Label the points R and S. A square is a quadrilateral with all four sides of the same length. After plotting the points, trace the square by connecting the points.

Answer 1

ANSWER and EXPLANATION

We want to plot two points to form a square.

So, we will have square PQRS with sides PQ, QR, RS and SP.

Because it is a square, we have that all the lines must be the same length.

Because each of the lines are perpendicular to one another, we will have that the slope of one will be the negative inverse of the preceeding line.

We will find one point R such that the line between that point and Q is perpendicular to PQ and another point S such that the line between that point and P is perpendicular to RS.

Negative inverse slope here is going to be applied in such a way that we invert the change in y and change in x between each line while alternating the negative sign.

From observing the line PQ, we see that the change of x and y from P to Q is:

(x + 2, y - 7)

i.e P(-4, 4) => Q(-4 + 2, 4 - 7) = Q(-2, -3)

Therefore, for the next point R, since the slope of QR is the negative inverse of PQ, it will become that the change from x and y from Q to R is:

(x + 7, y + 2)

i.e Q(-2, -3) => R(-2 + 7, -3 + 2) = R(5, -1)

The same principle applies for S, we use the negative inverse:

(x - 2, y + 7)

i.e R(5, -1) => S(5 - 2, -1 + 7) = S(3, 6)

Therefore, the two points are R(5, -1) and S(3, 6)

The graph is given below: