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Worksheet on Distance Between Two Factors



Drawback 1 :

Discover the gap between the 2 factors given beneath. 

(-12, 3) and (2, 5)

Drawback 2 :

Discover the gap between the 2 factors given beneath. 

(-2, -3) and (6, -5)

Drawback 3 :

If the gap between the 2 factors given beneath is 2√29, then discover the worth of ok, on condition that ok > 0.  

(-7, 2) and (3, ok)

Drawback 4 :

Discover the gap between the factors A and B within the xy-pane proven beneath. 

Drawback 5 :

The determine exhibits a proper triangle. Discover the size of the hypotenuse to the closest tenth.

Drawback 6 :

Gabriela needs to seek out the gap between her home on one facet of a lake and the seashore on the opposite facet. She marks off a 3rd level forming a proper triangle, as proven within the determine. The distances within the diagram are measured in meters. Discover the straight-line distance from Gabriela’s home to the seashore utilizing distance between two factors method. Verify your reply utilizing Pythagorean Theorem.

Solutions

1. Reply :

(-12, 3) and (2, 5)

Formulation for the gap between the 2 factors is

√[(x2 – x1)2 + (y2 – y1)2]

Substitute (x1, y1)  =  (-12, 3) and (x2, y2)  =  (2, 5).


√[(2 + 12)2 + (5 – 3)2]

 √[142 + 22]

=  
√[196 + 4]

= 
√200

=  
√(2 ⋅ 10 ⋅ 10)

=   10√2

So, the gap between the given factors is 10√2 models. 

2. Reply :

(-2, -3) and (6, -5)

Formulation for the gap between the 2 factors is

√[(x2 – x1)2 + (y2 – y1)2]

Substitute (x1, y1)  =  (-2, -3) and (x2, y2)  =  (6, -5).

 √[(6 + 2)2 + (-5 + 3)2]

 √[82 + (-2)2]

=   √[64 + 4]

=  √68

=   √(2 ⋅ 2 ⋅ 17)

=   2√17

So, the gap between the given factors is 2√17 models. 

3. Reply :

(-7, 2) and (3, ok)

Distance between the above two factors  =  2√29

√[(x2 – x1)2 + (y2 – y1)2]  =  2√29

Substitute (x1, y1)  =  (-7, 2) and (x2, y2)  =  (3, ok).

√[(3 + 7)2 + (k – 2)2]  =  2√29

√[102 + (k – 2)2]  =  2√29

√[100 + (k – 2)2]  =  2√29

Sq. either side. 

100 + (ok – 2)2  =  (2√29)2

100 + ok2 – 2(ok)(2) +  22  =  22(√29)2

100 + ok2 – 4k +  4  =  4(29)

ok2 – 4k + 104  =  116

Subtract 116 from either side.

ok2 – 4k – 12  =  0

(ok – 6)(ok + 2)  =  0

ok – 6  =  0  or  ok + 2  =  0

ok  =  6  or  ok  =  -2

As a result of ok > 0, we have now

ok  =  6

4. Reply :

Establish the factors A and B within the xy-plane above. 

Formulation for the gap between the 2 factors is

√[(x2 – x1)2 + (y2 – y1)2]

To seek out the gap between the factors A and B, substitute (x1, y1)  =  (2, -3) and (x2, y2)  =  (5, 5).  

AB  =  √[(5 – 2)2 + (5 + 3)2]

AB  =  √[32 + 82]

AB  =  √(9 + 64)

AB  =  √73 models

5. Reply :

Mark the required coordinates to seek out the size of the hypotenuse.  

Size of the hypotenuse :

=  √[(x2 – x1)2 + (y2 – y1)2]

Substitute (x1, y1)  =  (-1, -1) and (x2, y2)  =  (1, 3).  

=  √[(1 + 1)2 + (3 + 1)2]

=  √[22 + 42]

=  √(4 + 16)

=  √20

≈  4.5 models

6. Reply :

Straight-line distance from Gabriela’s home to the seashore (utilizing distance between two factors method) :

=  √[(x2 – x1)2 + (y2 – y1)2]

Substitute (x1, y1) = (10, 20) and (x2, y2) = (280, 164).

=  √[(280 – 10)2 + (164 – 20)2]

=  √[2702 + 1442]

=  √(72900 + 20736)

=  √93636

= 306 meters

Checking the reply utilizing Pythagorean Theorem :

Step 1 :

Discover the size of the horizontal leg.

The size of the horizontal leg is absolutely the worth of the distinction between the x-coordinates of the factors (280, 20) and (10, 20).

|280 – 10|  =  270

The size of the horizontal leg is 270 meters.

Step 2 :

Discover the size of the vertical leg.


The size of the vertical leg is absolutely the worth of the distinction between the y-coordinates of the factors (280, 164) and (280, 20).

|164 – 20|  =  144

The size of the vertical leg is 144 meters.

Step 3 :

Let a = 270, b = 144 and c symbolize the size of the hypotenuse. Use the Pythagorean Theorem to put in writing the connection between a, b and c.

a2 + b2  =  c2

Step 4 :

Substitute a  =  270 and b  =  144 and resolve for c. 

2702 + 1442  =  c2

Simplify.

72,900 + 20,736  =  c2

93,636  =  c2

Take the sq. root of either side.

93,636  =  √c2

306  =  c

So, the gap from Jose’ home to the seashore is 306 meters.

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