Complete the coordinate proof of the theorem. given: a b c d is a square. prove: the diagonals of a b c d are perpendicular. art: a square a b c d is graphed on a coordinate plane. the horizontal x-axis and vertical y-axis are solid. the vertex labeled as a lies on begin ordered pair 0 comma 0 end ordered pair. the vertex labeled as b lies on begin ordered pair a comma 0 end ordered pair. the vertices c and d are unlabeled. diagonal a c and b d are drawn by dotted lines. enter your answers in the boxes. the coordinates of square abcd are a(0, 0) , b(a, 0) , c(, a), and d(0, ). the slope of ac⎯⎯⎯⎯⎯ , when simplified, is equal to . the slope of bd⎯⎯⎯⎯⎯, when simplified, is equal to −1 . the product of the slopes is equal to . therefore, ac⎯⎯⎯⎯⎯ is perpendicular to bd⎯⎯⎯⎯⎯.

Since the square is on a quadrant plane and it is a square, the fact that the  lines cross in the center and start and stop in the corners allows you to tell that they are perpendicular.

So answer one is (B, D) 2 is (0, C) 3 is: 1

your answer is the frist one

hop i

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1