Find the distance between ( 3 4 , 4 ) \left( \frac { 3 } { 4 } , 4 \right) ( 4 3 , 4 ) and ( 3 4 , − 8 ) \left( \frac { 3 } { 4 } , - 8 \right) ( 4 3 , − 8 ) .A) 4B) 24C) 12 3 4 12 \frac { 3 } { 4 } 12 4 3 D) 12E) 4 3 4 4 \frac { 3 } { 4 } 4 4 3

Question

Find the distance between   ( 3 4 , 4 )  \left( \frac { 3 } { 4 } , 4 \right)  ( 4 3 ​ , 4 )    and   ( 3 4 , − 8 )  \left( \frac { 3 } { 4 } , - 8 \right)  ( 4 3 ​ , − 8 )    .A)  4B)  24C)    12 3 4 12 \frac { 3 } { 4 } 12 4 3 ​ D)  12E)    4 3 4 4 \frac { 3 } { 4 } 4 4 3 ​

Renee Deelstra · Accepted Answer

Final Answer : D, Explanation :   The distance between two points   ( x 1 , y 1 ) (x_1, y_1) ( x 1 ​ , y 1 ​ )   and   ( x 2 , y 2 ) (x_2, y_2) ( x 2 ​ , y 2 ​ )   in a plane is given by the formula   ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ( x 2 ​ − x 1 ​ ) 2 + ( y 2 ​ − y 1 ​ ) 2 ​  . Here, since the x-coordinates are the same (  3 4 \frac{3}{4} 4 3 ​  ), the distance is simply the difference in y-coordinates:   ∣ 4 − ( − 8 ) ∣ = ∣ 4 + 8 ∣ = 12 |4 - (-8)| = |4 + 8| = 12 ∣4 − ( − 8 ) ∣ = ∣4 + 8∣ = 12  .

Find the distance between $\left( \frac { 3 } { 4 } , 4 \right)$ and $\left( \frac { 3 } { 4 } , - 8 \right)$ .

A) 4
B) 24
C) $\frac { 3 } { 4 }$
D) 12
E) $\frac { 3 } { 4 }$

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Learning Objectives

Learning Objectives

Related questions

Find the distance between (34,4) \left( \frac { 3 } { 4 } , 4 \right) (43​,4) and (34,−8) \left( \frac { 3 } { 4 } , - 8 \right) (43​,−8) .A) 4B) 24C) 123412 \frac { 3 } { 4 }1243​ D) 12E) 4344 \frac { 3 } { 4 }443​

Definitions

Learning Objectives

Learning Objectives

Related questions

Find the distance between $\left( \frac { 3 } { 4 } , 4 \right)$ and $\left( \frac { 3 } { 4 } , - 8 \right)$ .

A) 4
B) 24
C) $\frac { 3 } { 4 }$
D) 12
E) $\frac { 3 } { 4 }$