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AlexFokin [52]
3 years ago
15

Find all points on the x-axis that are a distance 5 from P(-8,3)

Mathematics
1 answer:
ser-zykov [4K]3 years ago
8 0
On the x axis means that the y value is 0 or the point is (x,0)

distance formula

D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
we know that distance is 5
the first point is (x1,y1)
the (x2,y2) is (x,0)

so
D=5
x1=-8
y1=3
x2=x
y2=0

5=\sqrt{(-8-x)^2+(3-0)^2}
5=\sqrt{(-8-x)^2+(3)^2}
5=\sqrt{64+16x+x^2+9}
5=\sqrt{x^2+16x+73}
square both sides
25={x^2+16x+73}
minus 25 both sides
0=x^2+16x+48
factor
0=(x+4)(x+12)
set each to zero

x+4=0
x=-4

x+12=0
x=-12

the points are

(-4,0) and (-12,0)

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