Math Problem Statement

Find the distance between X(-3, 8) and Z(-5, 1). Round to the nearest tenth, if necessary.

Solution

To find the distance between points X(3,8)X(-3, 8) and Z(5,1)Z(-5, 1), we can use the distance formula:

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Given that:

X(3,8)=(x1,y1),Z(5,1)=(x2,y2)X(-3, 8) = (x_1, y_1), \quad Z(-5, 1) = (x_2, y_2)

Substituting into the distance formula:

d=((5)(3))2+(18)2d = \sqrt{((-5) - (-3))^2 + (1 - 8)^2}

Let's calculate this step by step.

d=(5+3)2+(18)2=(2)2+(7)2d = \sqrt{(-5 + 3)^2 + (1 - 8)^2} = \sqrt{(-2)^2 + (-7)^2}

d=4+49=537.3unitsd = \sqrt{4 + 49} = \sqrt{53} \approx 7.3 \, \text{units}

Thus, the distance between the two points is approximately 7.3 units.

Do you have any questions or would you like more details?


Here are five related questions for further exploration:

  1. How would you calculate the distance in 3D space between two points?
  2. What is the midpoint between points X(3,8)X(-3, 8) and Z(5,1)Z(-5, 1)?
  3. How does the Pythagorean theorem relate to the distance formula?
  4. If the coordinates of ZZ changed, how would the distance calculation change?
  5. How can we apply the distance formula to solve real-world problems?

Tip: When using the distance formula, be careful with signs when subtracting the coordinates to avoid errors in squaring.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Calculation

Formulas

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-10