Question

the distance between the points (10, -2) and (4, 6) is 10.
true
false

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, \( x_1 = 10 \), \( y_1 = -2 \), \( x_2 = 4 \), \( y_2 = 6 \).

Step3: Substitute into formula

Calculate \( (x_2 - x_1)^2=(4 - 10)^2=(-6)^2 = 36 \), \( (y_2 - y_1)^2=(6 - (-2))^2=(8)^2 = 64 \).

Step4: Sum and take square root

Sum: \( 36 + 64 = 100 \), square root: \( \sqrt{100}=10 \).

Answer:

True