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olchik [2.2K]
3 years ago
15

What are the 6 trigonometric functions of (4,-2) and (-9,-9)

Mathematics
1 answer:
butalik [34]3 years ago
8 0
<span>Finding the distance, midpoint, slope, equation and the x y-interceptsof a line passing between the two points p1 (4,-2) and p2 (-9,-9)</span>The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula<span><span>d = √</span><span> ((X2-X1)2+(Y2-Y1)2)</span></span><span><span>d = √</span><span>(-9-4)2+(-9--2)2</span></span><span><span>d = √</span><span>((-13)2+(-7)2)
</span></span><span><span>d = √</span><span>(169+49)
</span></span><span><span>d = √</span><span>218
</span></span>


The distance between the points is 14.7648230602334

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2
Xm=(4+-9)/2=-2.5

Find the Y value of the midpoint

Ym=(Y1+Y2)/2
Ym=(-2+-9)/2=-5.5

The midpoint is: (-2.5,-5.5)

Graphing the two points, midpoint and distance<span><span>P1 (4,-2)</span><span>P2 (-9,-9)</span>Midpoint (-2.5,-5.5)The length of the black line is the distance between the points (14.7648230602334)</span>


Find the slope of the line connecting the two points<span><span><span>Slope = </span><span>(Y2-Y1)</span> = (-9--2) = (-7) = 0.538461538461538</span><span><span>(X2-X1)</span>(-9-4)(-13)</span></span>Find the equation of the line passing through the two points

The general equation for a straight line isy = mx + b<span>Where </span>m<span> represents the slope of the line which we found in the previous </span>step<span> to be 0.538461538461538</span><span>y = 0.54x + b</span>We substitute x and y for the values from one of our points (4,-2)<span>-2 = .54×4 + b</span><span>-2 = 2.15 + b</span>-2-2.15 = b-4.15 = b<span>Knowing both </span>b<span> and </span>m, we can contruct the equation of the liney= 0.54x-4.15

X and Y interceptsThe x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y
y= 0.54x-4.150= 0.54x-4.15-0.54x= -4.15x= -4.15/-0.54 = 7.71The x intercept for this straight line is 7.71

The y-intercept is a point on the graph where x is zero


Using the equation we found in the previous step and substituting zero for x
y= 0.54×0-4.15y= -4.15The y intercept for this straight line is -4.15

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