hi
i will ask u in math :)
in (( distance between two points ))
* three vertices of rectanglr WXYZ are W (4,3), X (-1,3), and Y (-1,-1), what sre the coordinates of Z ?
** two adjacent vertices of a square have coordinates (-1,-3) and (1,0), what are the possible coordinates of the other two vertices ?
why there is no one answer my question ?
Give me answer of this question
Hi! I'd be happy to help you with your math questions.
To find the coordinates of point Z in rectangle WXYZ, we can use the fact that opposite sides of a rectangle are parallel, and equal in length.
First, let's find the length of WX and WY. We can use the distance formula, which is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
For WX:
x1 = 4, y1 = 3
x2 = -1, y2 = 3
Substituting these values into the formula, we get:
WX = √[(-1 - 4)^2 + (3 - 3)^2]
= √[(-5)^2 + (0)^2]
= √[25]
= 5
For WY:
x1 = 4, y1 = 3
x2 = -1, y2 = -1
Substituting these values into the formula, we get:
WY = √[(-1 - 4)^2 + (-1 - 3)^2]
= √[(-5)^2 + (-4)^2]
= √[25 + 16]
= √[41]
Since opposite sides of a rectangle are equal in length, WZ will also have a length of 5 and ZY will have a length of √41.
Now, let's find the coordinates of Z.
Point Z is on the same y-coordinate as W and Y (-1,3) and (-1,-1) respectively. Therefore, the x-coordinate of Z will be the same as theirs.
So, the coordinates of Z are (-1, 3 + √41).
Now, let's move on to the second question.
To find the possible coordinates of the other two vertices of a square, given two adjacent vertices, we need to consider the properties of a square.
A square has four equal sides and four 90-degree angles. The distance between two adjacent vertices represents the length of the sides of the square.
Using the distance formula, we can find the length of the sides of the square.
Given the two adjacent vertices:
x1 = -1, y1 = -3
x2 = 1, y2 = 0
Using the formula, we get:
d = √[(1 - (-1))^2 + (0 - (-3))^2]
= √[(2)^2 + (3)^2]
= √[4 + 9]
= √[13]
Since all sides of a square are equal, the lengths of the other two sides will also be √13.
Now, we need to find the possible coordinates of the other two vertices.
Given one adjacent vertex (-1, -3), we can determine the other possible vertices by adding and subtracting √13 from the x and y-coordinates.
So, the possible coordinates for the other two vertices are:
(-1 + √13, -3 - √13)
(-1 - √13, -3 + √13)
I hope this helps! Let me know if you have any more math questions.