Question

if the points A, B &C are (-7,0) (5,-5) (-1,8) respectively find AB +AC​

Answer 1

$Given : A(-7,0), B(5,-5) \:and \: C(-1,8) \:are\\three \: points .$

$\underline { \blue { Distance \: Formula :}}$

$\pink { The \:distance \: between \: two }$

$\pink { given \: points \: P(x_{1}, y_{1}) \:and }$

$\pink { Q(x_{2}, y_{2}) \: is :}$

$\boxed { \orange { PQ = \sqrt{ ( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }}}$

$i ) AB = \sqrt{ [5 - (-7)]^{2} + ( -5 - 0 )^{2}} \\= \sqrt{ (5+7)^{2} + 25 }\\= \sqrt{ (12)^{2} + 25 }\\= \sqrt{ 144+ 25 }\\= \sqrt{ 169 }\\= \sqrt{13^{2}}\\= 13 \:--(1)$

$ii ) AC = \sqrt{ [-1 - (-7)]^{2} + ( 8 - 0 )^{2}} \\= \sqrt{ (-1 +7)^{2} + 64 }\\= \sqrt{ (6)^{2} + 64 }\\= \sqrt{ 36+ 64 }\\= \sqrt{ 100 }\\= \sqrt{10^{2}}\\= 10 \:--(2)$

/* From ( 1 ) and (2) , we get */

$iii ) Value \: of \: AB + AC = 13 + 10 = 23$

Therefore.,

$\red {Value \: of \: AB + AC }\green {= 23}$

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