Question

for items 9 - 11, determine the length of each segment with the given endpoints.

1. c(1,4) and d(11,28)
2. y(-2,6) and z(5,-8)
3. p(-7,-7) and q(9,5)

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Step2: Solve for item 9

For points \(C(1,4)\) and \(D(11,28)\), \(x_1 = 1,y_1=4,x_2 = 11,y_2=28\)

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Step3: Solve for item 10

For points \(Y(-2,6)\) and \(Z(5,-8)\), \(x_1=-2,y_1 = 6,x_2=5,y_2=-8\)

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Step4: Solve for item 11

For points \(P(-7,-7)\) and \(Q(9,5)\), \(x_1=-7,y_1=-7,x_2=9,y_2 = 5\)

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Answer:

1. \(26\)
2. \(7\sqrt{5}\approx15.65\)
3. \(20\)