Question

what is the area of square efgh? area = square units

Explanation:

Step1: Find the length of side EF

Points E(-8, 2) and F(-1, 2) (wait, no, looking at the grid, E is at (-8,2), F is at (-1,2)? Wait, no, the x-coordinates: E is at x=-8, F is at x=-1? Wait, no, the grid lines: from E to F, how many units? Let's check the x-coordinates. E is at x = -8, F is at x = -1? Wait, no, the distance between E(-8,2) and F(-1,2)? Wait, no, maybe I misread. Wait, the square EFGH: E is (-8,2), F is (-1,2)? Wait, no, the horizontal distance: from x=-8 to x=-1? Wait, no, maybe the x-coordinate of F is -1? Wait, no, looking at the grid, the x-axis: from -10 to 10, each grid is 1 unit. So E is at (-8, 2), F is at (-1, 2)? Wait, no, the distance between E and F: the x-coordinates are -8 and -1? Wait, no, maybe F is at (-1,2)? Wait, no, the vertical distance: E is ( -8,2), H is (-8, -5)? Wait, no, H is at (-8, -5)? Wait, G is at (-1, -5)? Wait, let's calculate the length of EF: the x-coordinate of E is -8, x-coordinate of F is -1? Wait, no, the distance between E(-8,2) and F(-1,2) is |-1 - (-8)| = 7? Wait, no, maybe I made a mistake. Wait, looking at the grid, E is at (-8,2), F is at (-1,2)? Wait, no, the horizontal line from E to F: how many grid squares? From x=-8 to x=-1: that's 7 units? Wait, no, maybe F is at (-1,2)? Wait, no, the vertical side: E(-8,2) to H(-8,-5): the distance is |-5 - 2| = 7? Wait, no, H is at (-8, -5)? Wait, G is at (-1, -5). So the length of EF is the horizontal distance between E(-8,2) and F(-1,2): |-1 - (-8)| = 7? Wait, no, -1 - (-8) = 7? Wait, -1 +8 =7. So length is 7? Wait, no, maybe I misread the coordinates. Wait, E is at (-8,2), F is at (-1,2)? Wait, no, the x-coordinate of F: looking at the grid, the y-axis is at 0, so F is at x=-1? Wait, no, the grid lines: from -10 to 10, each line is 1 unit. So E is at x=-8, y=2; F is at x=-1, y=2? Wait, no, the distance between E and F: the x difference is (-1) - (-8) = 7, so length is 7. Then the vertical side: E(-8,2) to H(-8,-5): y difference is -5 -2 = -7, absolute value 7. So it's a square with side length 7? Wait, no, wait, H is at (-8, -5)? Wait, G is at (-1, -5). So the length of EH is from y=2 to y=-5: 2 - (-5) =7. So side length is 7. Then area of square is side squared: 77=49? Wait, no, wait, maybe I made a mistake. Wait, let's check the coordinates again. E is (-8,2), F is (-1,2): distance is |-1 - (-8)| =7. E is (-8,2), H is (-8,-5): distance is |-5 -2|=7. So it's a square with side length 7. So area is 77=49. Wait, but maybe the coordinates are different. Wait, maybe F is at (-1,2), G is at (-1,-5), H is (-8,-5), E is (-8,2). So the length of EF is from x=-8 to x=-1: 7 units. Length of EH is from y=2 to y=-5: 7 units. So area is 7*7=49.

Step1: Determine side length

Find the horizontal distance between E(-8, 2) and F(-1, 2). The distance formula for horizontal points (same y - coordinate) is \( |x_2 - x_1| \). So \( |-1 - (-8)| = |7| = 7 \). So the side length of the square is 7 units.

Step2: Calculate area of square

The area of a square is given by \( \text{side length}^2 \). So \( 7^2 = 49 \).

Answer:

49