Question

find the distance between the coordinates given. *
10 g(1, -4), h(9,2)
your answer

find the distance between the coordinates given. *
11 d(5,6), e(-3,8)
your answer

Explanation:

Problem 10: Distance between \( G(1, -4) \) and \( H(9, 2) \)

Step 1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step 2: Identify the coordinates

Here, \( x_1 = 1 \), \( y_1 = -4 \), \( x_2 = 9 \), \( y_2 = 2 \).

Step 3: Substitute into the formula

First, calculate the differences: \( x_2 - x_1 = 9 - 1 = 8 \), \( y_2 - y_1 = 2 - (-4) = 6 \).
Then, square these differences: \( 8^2 = 64 \), \( 6^2 = 36 \).
Add them: \( 64 + 36 = 100 \).
Take the square root: \( \sqrt{100} = 10 \).

Step 1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step 2: Identify the coordinates

Here, \( x_1 = 5 \), \( y_1 = 6 \), \( x_2 = -3 \), \( y_2 = 8 \).

Step 3: Substitute into the formula

Calculate the differences: \( x_2 - x_1 = -3 - 5 = -8 \), \( y_2 - y_1 = 8 - 6 = 2 \).
Square these differences: \( (-8)^2 = 64 \), \( 2^2 = 4 \).
Add them: \( 64 + 4 = 68 \).
Take the square root: \( \sqrt{68} = 2\sqrt{17} \approx 8.246 \) (if a decimal approximation is needed, but the exact form is \( 2\sqrt{17} \)).

Answer:

10

Problem 11: Distance between \( D(5, 6) \) and \( E(-3, 8) \)