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Chapter 11: Q. 12 (page 1082)

In the following exercises, find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

(-4,-5)and(7,4).

Short Answer

Expert verified

The distance between the points is14.2.

Step by step solution

01

Step 1. Given and explanation.

We have the points as (-4,-5)and(7,4).

The formula for distance between two points, i.e., (x1,y1),(x2,y2)is-

d=(x2-x1)2+(y2-y1)2.

Using this formula, we can calculate the distance.

02

Step 2. Applying the formula.

Consider the point (-4,-5)as (x1,y1)and (7,4)as (x2,y2).

Substituting the values in the distance formula gives us,

d=7-(-4)2+4-(-5)2d=7+42+4+52

03

Step 3. Simplifying the radical.

We have d=(7+4)2+(4+5)2.

Simplifying it,

d=(11)2+(9)2d=121+81d=202d鈮�14.2
Thus we get the distance as14.2

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