Question

Give coordinates for three possible pairs of points for the other two verticies...

Answer 1

Answer:

A) (-1,3) and (4,3)

B) (-1,-7) and (4,-7)

C) (1.5, .5) and (1.5, -4.5)

Step-by-step explanation:

For 1 and 2, because the y-values of the points are the same, the length of the square can be found by subtracting the x-coordinates.

4-(-1)=4+1=5

The length of the side of the square is 5.

1. For the first set of points, the square is above the two given points so just add 5 to the y-values

-2+5=3

This gives you the points:

(-1,3) and (4,3)

2. For the second set of points, the square is below the two given points so subtract 5 from the y-values.

-2-5=-7

This give you the points:

(-1,-7) and (4,-7)

3. The third answer is when the two given points are on opposite corners

of the square.

Here the diagonal is equal to 5 since they are on opposite corners of the square.

The diagonal of a square can be found with the pythagorean theorem

Since we have the diagonal we can find the side lengths we need.

$2s^2=25$

s=$\sqrt{\frac{25}{2} }$

s=3.5355

We want the new vertices to be in the middle of the other vertices x-coordinates

$\frac{4-(-1)}{2} =\frac{5}{2} =2.5$

The new vertices will be 2.5 units away from the other vertices

-1+2.5=1.5

The new vertices will be at x=1.5

Now we need the pythagorean theorem again to find the y-values

$(2.5)^2+h^2=(3.5355)^2$

$6.25+h^2=\frac{25}{2}$

$h=\sqrt{\frac{25}{2} -6.25}$

h=2.5

The new vertices will be:

(1.5, -2+2.5)=(1., .5)

(1.5, -2-2.5)=(1.5, -4.5)