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pishuonlain [190]
3 years ago
8

What is the distance between (2, -1) and (-1, -5) on the coordinate plane?

Mathematics
2 answers:
Gekata [30.6K]3 years ago
6 0

C. 5 units is the answer and I am typing to make in 20 characters long.

Ipatiy [6.2K]3 years ago
4 0

you can use this formula:

d =  \sqrt{ {(xa - xb)}^{2} -  {(ya - yb)}^{2}}

a=(2,-1) and. b=(-1,-5)

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1. Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the
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#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never

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#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1).  First we simplify our equation using the distributive property:

y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

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y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

Subtract 2x from each side"

2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2.  To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2.  Using point-slope form,

y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}

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#5) Two lines with the same slope are always parallel.  They are never perpendicular.

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