Question

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

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.