Math  /  Geometry

QuestionIn Exercises 32-33, find the exact distance between the two points.
32. G(1,5)G(-1,-5) and H(3,8)GH=H(3,-8) \quad G H= \qquad
33. G(2,5)G(2,5) and H(4,1)GH=H(4,-1) G H= \qquad

Use the information to find the midpoint between points AA and BB. In a three-dimensional coordinate system, the midpoint between A(x1,y1,z1)A\left(x_{1}, y_{1}, z_{1}\right) and B(x2,y2,z2)B\left(x_{2}, y_{2}, z_{2}\right) is (x1+x22,y1+y22,z1+z22)\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}, \frac{z_{1}+z_{2}}{2}\right).
34. A(3,0,4)A(-3,0,4) B(7,2,8)B(7,2,8)

Use the information to find the distance between points AA and BB. Leave answers in simplified radical form. In a threedimensional coordinate system, the distance between the two points A(x1,y1,z1)A\left(x_{1}, y_{1}, z_{1}\right) and B(x2,y2,z2)B\left(x_{2}, y_{2}, z_{2}\right) is AB=(x2x1)2+(y2y1)2+(z2z1)2A B=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}
35. A(2,1,2)A(-2,1,2) B(2,3,4)B(2,-3,4)

Studdy Solution
Sum the squares and take the square root. d=36 d = \sqrt{36} d=6 d = 6
Solution:
1. The distance between G(1,5)G(-1,-5) and H(3,8)H(3,-8) is 55.
2. The distance between G(2,5)G(2,5) and H(4,1)H(4,-1) is 2102\sqrt{10}.
3. The midpoint between A(3,0,4)A(-3,0,4) and B(7,2,8)B(7,2,8) is (2,1,6)(2, 1, 6).
4. The distance between A(2,1,2)A(-2,1,2) and B(2,3,4)B(2,-3,4) is 66.

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