Find the length of the longest side of the rectangle whose vertices are given. a(2, 1), b(5, 4), c(0, 3), d(3, 6)
1 answer:
First, you plot the coordinates to visualize the problem clearly. As you can see in the picture, the longest sides could either be one of those marked in red. This could be initially determined when you use visual estimation. We measure this using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2)]
Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units
Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units
They are of equal length. Both are the longest sides which measures 4.24 units.
Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units
Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units
They are of equal length. Both are the longest sides which measures 4.24 units.
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Considering the definition of perpendicular line, the equation of of perpendicular line is y= -x +
.
A linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.
m is the slope.
b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
<h3>Perpendicular line</h3>Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
<h3>Equation of perpendicular line in this case</h3>In this case, the line is 2x-y=8. Expressed in the form y = mx + b, you get:
-y=8 - 2x
y= (-2x +8)÷ (-1)
y= 2x -8
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of 2. So:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (2)
<u><em>slope perpendicular line= -</em></u>
So, the perpendicular line has a form of: y= -x + b
The line passes through the point (9, 2). Replacing in the expression for perpendicular line:
2= (-)× 9 + b
2= - + b
2+ = b
<u><em /></u><u><em>= b</em></u>
Finally, the equation of of perpendicular line is y= -x +
.
Learn more about perpendicular line:
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