Answer :

altavistard

Answer:

11.2 units

Step-by-step explanation:

From (-7, -7) to (-2, 3) is 5 units horizontally  and  10 units vertically.  Thus we have a right triangle with sides 5 and 10 respectively.  The length of the hypotenuse of this triangle is the distance between (-2, 3) & (-7, -7):

d = √(5² + 10²) = √(25 + 100) = √125 = √25√5, or 5√5.

This is approximately 11.2 units

AmiAblePshYcO

[tex]{ \sf{find \: the \: distance \: between \: ( - 2,3)and \: ( - 7, - 7).}} \\ { \sf{round \: to \: the \: nearest \: tenth}}[/tex]

[tex]{ \sf{ \red{distance = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } }}} \\ \\ { \sf{x1 = - 2}} \\ { \sf{x2 = - 7}} \\ { \sf{y1 = 3}} \\ { \sf{ y2 = - 7}}[/tex]

[tex]{ \sf{ \green{ distance = \sqrt{ {( - 7 - ( - 2)})^{2} + {( - 7 - 3)}^{2}}}} } \\ \\ { : {\implies{ \green{ \sf{distance = \sqrt{ {( - 5)}^{2} + {( - 10)}^{2} } }}}}} \\ \\ { : { \implies{ \green{ \sf{distance = \sqrt{25 + 100}}}}}} [/tex]

[tex]{ : { \implies{ \sf{ \green{distance = \sqrt{125}}}}}} \\ \\ { : { \implies{ \green{ \sf{distance = 5 \sqrt{5}}}}}} \\ \\ { : { \implies{ \green{ \sf{distance = 5 \times 2.236}}}}}[/tex]

[tex]{ : { \implies{ \underline{ \green { \sf{distance = 11.18= 11.2}}}}}}[/tex]

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