Question

16. Find the value of y, if the distance between points (2,-3) & (10,y) is 10 units.


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Answer 1

Solution:

• Here,The distance between the points (2,-3) and (10,y) is 10 units.so that we can use the formula of distance between two points to find the value of y.

$\\ \underline{\dag\;\frak{As\;we\;know\;that:}} \\ \\ \green{ \bigstar} \: \fbox{\sf{Distance\;between\;points\;=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}$

Applying the values,

$\\ \implies\sf{10 = \sqrt{{\bigg(10 - 2 \bigg)}^{2} + {\bigg(y - ( - 3) \bigg)}^{2} }} \\ \\ \implies\sf{10 = \sqrt{{\bigg(10 - 2 \bigg)}^{2} + {\bigg(y + 3 \bigg)}^{2}}} \\ \\ \implies\sf{10 = \sqrt{{ \bigg(8 \bigg)}^{2} + { \bigg(y + 3 \bigg)}^{2} }} \\ \\ \implies\sf{{10}^{2} = 64 + {(y + 3)}^{2}} \\ \\ \implies\sf{100 = 64 + {(y + 3)}^{2}} \\ \\ \implies\sf{100 - 64 ={(y + 3)}^{2}} \\ \\ \implies\sf{36 = {(y + 3)}^{2}} \\ \\ \implies\sf{ \sqrt{36} = (y + 3)} \\ \\ \implies\sf{ \pm \: 6 =y + 3} \\ \\ \implies\sf{y = \pm \: 6 + 3} \\ \\ \implies \underline{\boxed{\frak{y = - 9(or)3}}} \: \red{ \bigstar} \:$

Hence,

• The value of y is -9(or)3.

Answer 2

Given :-

• Coordinates of A = ( 2 , - 3 )
• Coordinates of B = ( 10 , y )
• Distance of AB = 10 units

To Find :-

• Value of y

Solution :-

By using distance formula

$\large\red \bigstar \: \boxed{ \green{\bf Distance = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }}$

Substitute values in formula

$\longmapsto \sf{10 = \sqrt{{\bigg(10 - 2 \bigg)}^{2} + {\bigg(y - ( - 3) \bigg)}^{2} }}$

$\longmapsto\sf{10 = \sqrt{{\bigg(10 - 2 \bigg)}^{2} + {\bigg(y + 3 \bigg)}^{2}}}$

$\longmapsto\sf{10 = \sqrt{{ \bigg(8 \bigg)}^{2} + { \bigg(y + 3 \bigg)}^{2} }}$

$\longmapsto\sf{{10}^{2} = 64 + {(y + 3)}^{2}}$

$\longmapsto\sf{100 = 64 + {(y + 3)}^{2}}$

$\longmapsto\sf{100 - 64 ={(y + 3)}^{2}}$

$\longmapsto\sf{36 = {(y + 3)}^{2}}$

$\longmapsto\sf{ \sqrt{36} = (y + 3)}$

$\longmapsto\sf{ \pm \: 6 =y + 3}$

$\longmapsto\sf{y = \pm \: 6 + 3}$

$\longmapsto \underline{\boxed{\frak{y = - 9(or)3}}} \: \red{ \bigstar} \:$

Hence,

The value of y is -9 , 3