Question
Given the vertices A(−2,4), B(1,4), and C(1,1), find the other vertex that is needed to construct the square.(1 point)
Answers
Answered by
GPT 3.5
To construct a square, all sides must be equal in length and all angles must be 90 degrees.
Starting with vertices A(-2,4), B(1,4), and C(1,1), we can find the length of side AB.
Using the distance formula, the distance between two points (x1,y1) and (x2,y2) is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
For side AB:
dAB = √[(1 - (-2))^2 + (4 - 4)^2]
= √[3^2 + 0^2]
= √9
= 3
Since a square has equal sides, the length of side AB is 3.
To find the other vertex, we need to find a point that is 3 units away from point B. Since point C(1,1) is already given, we know that point C is 3 units away from point B.
Thus, the other vertex needed to construct the square is D, which is 3 units to the left of point C.
Using the x-coordinate of C(1,1) and moving 3 units to the left, we get the x-coordinate of D(-2,1).
Therefore, the other vertex needed to construct the square is D(-2,1).
Starting with vertices A(-2,4), B(1,4), and C(1,1), we can find the length of side AB.
Using the distance formula, the distance between two points (x1,y1) and (x2,y2) is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
For side AB:
dAB = √[(1 - (-2))^2 + (4 - 4)^2]
= √[3^2 + 0^2]
= √9
= 3
Since a square has equal sides, the length of side AB is 3.
To find the other vertex, we need to find a point that is 3 units away from point B. Since point C(1,1) is already given, we know that point C is 3 units away from point B.
Thus, the other vertex needed to construct the square is D, which is 3 units to the left of point C.
Using the x-coordinate of C(1,1) and moving 3 units to the left, we get the x-coordinate of D(-2,1).
Therefore, the other vertex needed to construct the square is D(-2,1).