ABCD is a rectangle with B(-4,2) andD (10, 6). find the coordinates of A. Please help and tell me how you got it so I can understand
To find the coordinates of point A in the rectangle ABCD, we can use the fact that a rectangle has two pairs of opposite sides that are equal in length and parallel to each other.
Given that B(-4, 2) is a point on the rectangle, we can use the coordinates of B and the length of the sides to determine the coordinates of A.
First, let's find the length of side AB. The length of a line segment can be found using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, x1 = -4, y1 = 2 (coordinates of B), and x2 = ?, y2 = ? (coordinates of A). Since AB is a side of a rectangle, we know that the length of AB is equal to the length of CD.
So, let's find the length of CD using the distance formula:
CD (length of side AB) = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(10 - (-4))^2 + (6 - 2)^2]
= √[(14)^2 + (4)^2]
= √[196 + 16]
= √212
Now that we know the length of AB, we can use point B and the length of AB to find the coordinates of A. Since AB is horizontal, the x-coordinate of A will be equal to the x-coordinate of B plus the length of AB. Using B(-4, 2) and the length of AB (√212), we can calculate the x-coordinate of A:
x-coordinate of A = x-coordinate of B + length of AB
= -4 + √212
For the y-coordinate of A, we know that A and B have the same y-coordinate because they lie on the same horizontal line. Therefore, the y-coordinate of A will be 2.
So, the coordinates of point A are (-4 + √212, 2).