Question

find the distance between the points (-4, 10) and (-10, 2). round decimals to the nearest tenth. units

Explanation:

Step1: Recall the distance formula

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

Step2: Identify the coordinates

Let \( (x_1, y_1) = (-4, 10) \) and \( (x_2, y_2) = (-10, 2) \).

Step3: Substitute into the formula

Calculate \( x_2 - x_1 = -10 - (-4) = -10 + 4 = -6 \) and \( y_2 - y_1 = 2 - 10 = -8 \).
Then, \( d = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \)? Wait, no, wait: Wait, \( (-6)^2 = 36 \), \( (-8)^2 = 64 \), sum is \( 36 + 64 = 100 \), square root of 100 is 10? Wait, but let me check again. Wait, \( x_1 = -4 \), \( x_2 = -10 \), so \( x_2 - x_1 = -10 - (-4) = -6 \). \( y_1 = 10 \), \( y_2 = 2 \), so \( y_2 - y_1 = 2 - 10 = -8 \). Then squaring those: \( (-6)^2 = 36 \), \( (-8)^2 = 64 \). Sum is \( 36 + 64 = 100 \). Square root of 100 is 10. Wait, but the graph: let's check the horizontal distance between -4 and -10: that's 6 units (since from -10 to -4 is 6 units to the right). Vertical distance between 10 and 2: that's 8 units down. So it's a right triangle with legs 6 and 8, hypotenuse is 10 (since 6-8-10 is a Pythagorean triple). So the distance is 10.

Answer:

10