Please help me with this. Thanks! On a coordinate system, the lines containing two sides of a square have equations y=x and y=x+2. If the points at (0,0) and (0,2) are two of the vertices of the square, write equations for the lines containing the other two sides and find the coordinates of the other two vertices.
2007-01-17 04:16:44 · 4 answers · asked by katerina 1 in Science & Mathematics ➔ Mathematics
Two sides of the square are represented by y=x and y=x+2
(0,0) and (0,2) are two of the vertices
Both lie on y=x and y=x+2 respectively
The position of the given vertices tells us that they are diagonally opposite from the fact that the line connecting them (Y-axis) is inclined at 45º to the given lines
The other diagonal is the parallel to X axis and bisects the first diagonal at (0,1)
Thus equation of the diagonal is y=1
Other 2 vertices lie on it!
Thus the other vertices are (-1,1) and (1,1)
2007-01-17 04:19:55 · answer #1 · answered by Som™ 6 · 0⤊ 0⤋
First, I researched the definition of vertices. Looking at answers.com, I found the definition to be, the plural of vertex. I then look at the definition of vertex and found three possibilities for a mathematical definition:
The point at which the sides of an angle intersect.
The point on a triangle or pyramid opposite to and farthest away from its base.
A point on a polyhedron common to three or more sides.
The first option, "the point at which the sides of an angle intersect", is the one that applies in this problem.
I then sketched the coordinate systems as described including the two vertices and the two equations.
I saw from the sketch that these vertices on these lines were opposite of each other rather than adjacent and was able to pick out by observation that the other two vertices are
(-1, 1) and (1,1).
The equations for the lines containing the other two sides can be determined by using the pairs of points that lie on the other two lines, namely (-1,1) and (0,0) and (1,1) and (0,2).
Using the definition of a line's equation to be y = mx + b, where m is the slope and is equal to (y2 - y1) / (x2-x1) and b is the x-intercept and is equal to y when x = 0, I found the equations to be
y = -x and y = -x + 2.
2007-01-17 12:45:19 · answer #2 · answered by John 2 · 0⤊ 0⤋
y=-x n y=-x+2
2007-01-17 12:26:11 · answer #3 · answered by well thts it...... 3 · 0⤊ 0⤋
The lines are at a 45° diagonal, so your two given points (both on the y-axis) must be opposite corners. If you graph this you'll see that your two other corners are (-1,1) and (1,1). From here, you can set up the equations of the two other lines.
2007-01-17 12:23:00 · answer #4 · answered by Anonymous · 0⤊ 0⤋