Question

Problem-Solving: (Show your solutions)

1. The coordinates of the endpoint of ST are (-2,3) and (3,y), respectively.
Supposed the distance between S and T is 13 units. What value/s of y would satisfy the given condition. Justify your answer.


Please help me ineed it now
Please answer it correctly thank you ^_^​

Answer 1

Answer:-

Given:-

Distance between two points S(- 2 , 3) & T(3 , y) = 13 units.

We know that,

Distance between two points (x₁ , y₁) & (x₂ , y₂) is

$\red{\sf \: \sqrt{ {(x_2 - x_1)}^{2} + ( {y_2 - y_1)}^{2} }}$

Let,

• x₁ = - 2
• y₁ = 3
• x₂ = 3
• y₂ = y.

So,

According to the question;

$\implies \sf \: \sqrt{ {(3 - ( - 2))}^{2} + {(y - 3)}^{2} } = 13$

On squaring both sides we get,

$\implies \sf \: \bigg( \sqrt{ {(3 + 2)}^{2} + {(y - 3)}^{2} } \bigg) ^{2} = 13^{2} \\ \\ \\ \implies \sf \: {5}^{2} + {(y - 3)}^{2} = 169$

Using (a - b)² = a² + b² - 2ab we get,

$\: \implies \sf \:25 + {y}^{2} + 9 - 6y = 169 \\ \\ \\ \implies \sf \: {y}^{2} - 6y + 34 - 169 = 0 \\ \\ \\ \implies \sf \: {y}^{2} - 6y - 135 = 0 \\ \\ \\ \implies \sf \: {y}^{2} + 9y - 15y - 136 = 0 \\ \\ \\ \implies \sf \:y(y + 9) - 15(y + 9) = 0 \\ \\ \\ \implies \sf \:(y + 9)(y - 15) = 0 \\ \\ \\ \implies \boxed{ \sf \:y = - 9 \: ,\: 15}$

∴ The values of y are - 9 & 15 to satisfy the given condition.

Answer 2

Given :-

The coordinates of the endpoint of ST are (-2,3) and (3,y), respectively.

Supposed the distance between S and T is 13 units.

To Find :-

Value of y

Solution :-

By using distance formula

$\sf D = \sqrt{\bigg(x_2-x_1\bigg)^2 + \bigg(y_2-y_1\bigg)^2$

$\sf D^2 ={ \sqrt{\bigg(x_2 - x_1\bigg)^2 + \bigg(y_2 - y_1\bigg)^2}^2$

$\sf 13^2 = \bigg(3 - \{-2\}\bigg)^2 + \bigg(y-3\bigg)^2$

$\sf 169 = \bigg(3+2\bigg)^2 + \bigg(y-3\bigg)^2$

$\sf 169 = \bigg(5\bigg)^2 + \bigg(y-3\bigg)^2$

$\sf 169 = 25 + \bigg(y-3\bigg)^2$

$\sf 169-25= \bigg(y-3\bigg)^2$

$\sf 144 = \bigg(y - 3\bigg)^2$

$\sf \sqrt{144} = \sqrt{\bigg(y-3\bigg)^2}$

$\sf \pm 12 = y -3$

$\sf \pm 12 + 3 = y$

$\sf 15,-9=y$

Value of y = 15,-9