Posts Tagged ‘distance formula’

Problem 512

What is the distance between points P(10, 7) and Q(1, 8)?

 

Solution:-

 

Use the Distance Formula

 

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

 

d = \sqrt{(1-10)^2+(8 -7)^2}

 

d = \sqrt{81+1}

 

d = \sqrt{82}

Problem 511

What is the distance between points P(6, -2) and Q(3, 4)?

 

Solution:-

 

Use the Distance Formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

 

d = \sqrt{(3-6)^2+(4-(-2))^2}

 

d = \sqrt{9+36}

 

d = \sqrt{45}

 

d = 3\sqrt{5}

Problem 510

What is the distance between P(0, 0) and Q(5, 12)?

 

Solution:-

 

Use the Distance Formula

 

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

 

d = \sqrt{(5-0)^2+(12-0)^2}

 

d = \sqrt{25+144}

 

d = \sqrt{169}

 

d = 13

Problem 509

What is the distance between P(7, 0) and Q(8, 0)?

 

Solution:-

Use the Distance Formula

 

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}

 

d = \sqrt{(8-7)^2+(0-0)^2}

 

d  = 1

Find the distance between the pair of points.

Find  the distance between the pair of points.

Give an exact answer and an approximation to three decimal places.

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

 

Solution:-

 

To find the distance between two points, use the distance formula below.

d =  \sqrt{( x_{2}- x_{1})^2+( y_{2}- y_{1})^2}.

Substitute the value and calculate.

d =  \sqrt{( 2-(-5))^2+( -3-6)^2}

=\sqrt{(7)^2+(-9)^2}

= \sqrt{130}

This is the exact value of the distance between the two point.

Now find the approximate distance to three decimal places.

\sqrt{130}  \approx 11.402

 

Distance Formula

Distance Formula

 

The distance between the points (x1, y1) and (x2, y2) is

d = \sqrt{(x_{2}- x_{1})^{2}+(y_{2}- y_{1})^{2}} .

Distance between Two points (Two Dimensions)

Distance between Two points (Two Dimensions) :

Let P(x_1,y_1) and Q(x_2,y_2) are two points in a plane,distance between them is d.

Now we have to find the distance d, draw two perpendiculars on x axes from P and Q points, which are PM and QN, now draw a perpendicular PR from point P on QN.

distance formula

According to the above figure:

OM =x_1 ; PM = y_1

ON = x_2 ; QN = y_2

So PR = MN = ON – OM = x_2 -x_1

And QR = QN – RN  = QN – PM = y_2 -y_1

Now In right triangle PRQ :

PQ = \sqrt{PR^2 + QR^2}

Or PQ = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Or d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}  ….( distance formula)