(-2, 1)
(4,3)
0
"-
T
"+
х
Put the steps in order to find the distance between these 2 points.
(7 points)
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Use the Pythagorean Theorem for right triangles to determine the diagonal
length: 22 +62 = c²
:: 40
=
c²
:: Draw a right triangle by dropping a vertical side and a horizontal side.
::
40 =
40 is between √36 and √49, so between 6 and 7 - closer to 6, so about
6.3 units
::
Determine the vertical side (2 units) and horizontal side (6 units) lengths by
counting on the grid (be careful of the scale), or using the vertical
coordinates (3 to 1) and horizontal coordinates (-2 to 4).
:: 4+36= c²
Step 1: Use the Pythagorean Theorem to find the diagonal length: 2² + 6² = c²
Step 2: Calculate 4 + 36 = c²
Step 3: Simplify the equation to get 40 = c²
Step 4: Take the square root of both sides to find c: c ≈ √40
Step 5: Determine that c is between √36 and √49, closer to 6.3
Step 6: Find the vertical side length by counting points on the grid: 3 - 1 = 2
Step 7: Find the horizontal side length by counting points on the grid: 4 - (-2) = 6
Therefore, the distance between the two points is approximately 6.3 units.