Question

4 the coordinates for three vertices of a rectangle are (2, 2), (8, 2), and (2, 6). what are the coordinates of the fourth vertex? a. (2, 8) b. (8, 6) c. (4, 2) d. (8, 8)

Explanation:

Question 4

Step1: Analyze rectangle properties

In a rectangle, opposite sides are equal and parallel, so the x - coordinate of the fourth vertex should be the same as the x - coordinate of the vertex \((8,2)\) (since \((2,2)\) and \((2,6)\) have the same x - coordinate, so the other pair of vertices should have the same x - coordinate), and the y - coordinate should be the same as the y - coordinate of the vertex \((2,6)\) (since \((2,2)\) and \((8,2)\) have the same y - coordinate, so the other pair of vertices should have the same y - coordinate).

Step2: Determine the coordinates

The x - coordinate from \((8,2)\) is \(8\), and the y - coordinate from \((2,6)\) is \(6\). So the coordinates of the fourth vertex are \((8,6)\)? Wait, wait, let's re - check. Wait, \((2,2)\) and \((8,2)\) are on the same horizontal line (y = 2), length is \(8 - 2=6\). \((2,2)\) and \((2,6)\) are on the same vertical line (x = 2), length is \(6 - 2 = 4\). So the fourth vertex should have x - coordinate \(8\) (same as \((8,2)\)) and y - coordinate \(6\) (same as \((2,6)\))? Wait, no, the option b is \((8,6)\) (I think there was a typo in the original, maybe the option b is \((8,6)\)). Wait, the given options: a. \((2,8)\), b. \((8,6)\) (assuming the typo), c. \((6,2)\), d. \((8,8)\). So using the property of rectangles: in a rectangle \(ABCD\), if \(A=(2,2)\), \(B=(8,2)\), \(C=(2,6)\), then \(D\) should have \(x = 8\) (same as \(B\)) and \(y = 6\) (same as \(C\)), so \(D=(8,6)\), which is option b.

Line graphs are used to display data that changes over time or continuous data with a relationship between two quantitative variables. Categorical data (data that can be divided into groups or categories) is better displayed using bar graphs, pie charts, etc. So the statement "Categorical data should be displayed on a line graph" is False.

Answer:

b. \((8,6)\) (assuming the typo in the original option b, if the original option b is \((8,6)\))

Question 5