Question

The distance between (1,2)and (-2,k)is 5 find the value of k​

Answer 1

Question : The distance between (1,2)and (-2,k)is 5 find the value of k​

Formula used : $\sqrt{(x_2 - x_1)^{2}+(\sqrt{y_2 -y_1} )^{2}}$ = 5

Answer:    k = 6

Explanation:

points, $x_1=1,y_1=2,x_2=-2,y_2=k$

Now substitute these points in the formula,

$\sqrt{(x_2 - x_1)^{2}+(\sqrt{y_2 -y_1} )^{2}}=5\\\\\sqrt{(-2 - 1)^{2}+(k-2 )^{2}}=5\\\\=>\sqrt{(-3)^{2}+(k-2)^{2}}=5\\\\ =>(-3)^{2}+(k-2)^{2}=25\\\\=>(k-2)^{2}=25-9\\\\=>(k-2)^{2}=16\\\\=>(k-2)^{2}=4^{2}\\\\=> k-2=4\\\\=>k=6$

Hope helps u and mark brainliest plz

Answer 2

♚Question:

The distance between (1,2)and (-2,k)is 5 find the value of k

♚Answer:

⇴Let the points be A And B.

Given A and B is 5

By using, Distance formula,

$\large{ \boxed{ \red{ \bold{D {\tiny{AB}} \: = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } }}}}$

We have, A(1,2) and B(-2,k)

And, Distance between A and B= 5,

Then,

$⇢ \large{ \sf{{5 \: = \sqrt{( - 2 - 1) {}^{2} + (k - 2) {}^{2} } }}} \\ \sf{ \green{ \underline{ \underline{ \dag{ \: \: squaring \: both \: sides}}}}} \\ \\ ⇢ \large{ \sf{ \: 25 = {( - 2 - 1)}^{2} + (k - 2) {}^{2} }} \\ ⇢ \large{ \sf{ \: 25 = ( - 3) {}^{2} + (k - 2) {}^{2} }} \\ ⇢ \large{ \sf{ \: 25 = 9 + (k - 2) {}^{2} }} \\ ⇢\large{ \sf{ \: 16 = (k - 2) {}^{2} }} \\ ⇢\large{ \sf{ \: k - 2 = \pm{4}}} \\ \\ \large{ \bold{ \boxed{ \pink{case - 1}}}} \\⇢ \large{ \sf{k - 2= + 4}} \\ ⇢ \large{ \sf{ \boxed{k = 6}}} \\ \\ \large{ \bold{ \boxed{ \pink{case - 2}}}} \\ ⇢ \large{ \sf{k - 2 = - 4}} \\ ⇢ \large{ \sf{ \boxed{k = - 2}}}$

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♚So final answer:

$\huge{ \boxed{ \bold{ \red{k = 6 \: or \: - 2}}}}$