Question

Урок 69 3. Знайдіть відстань (в одиничних вiдрiзках) в початку коорд нат до кожноï з точок: A(3, 7) ; B(- 7, 8) C(-100);D(315,6) D(315,6);E(0);K(- 1 2 );F(4 3 5 ) .​

Answer 1

Ответ:

Пошаговое объяснение:

A(3, 7)        3.7

B(- 7, 8)      7.8

C(-100)      100

D(315,6)     315.6

E(0)            0

K(- 1 2 )       12

F(4 3 5 )    435

Answer 2

Finding the Distance in Coordinate Plane

To find the distance between two points in a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Let's calculate the distances between the given points:

1. Distance between point A(3, 7) and the origin (0, 0): - Using the distance formula: d = sqrt((3 - 0)^2 + (7 - 0)^2) d = sqrt(3^2 + 7^2) d = sqrt(9 + 49) d = sqrt(58) d ≈ 7.62

2. Distance between point B(-7, 8) and the origin (0, 0): - Using the distance formula: d = sqrt((-7 - 0)^2 + (8 - 0)^2) d = sqrt((-7)^2 + 8^2) d = sqrt(49 + 64) d = sqrt(113) d ≈ 10.63

3. Distance between point C(-100, 0) and the origin (0, 0): - Using the distance formula: d = sqrt((-100 - 0)^2 + (0 - 0)^2) d = sqrt((-100)^2 + 0^2) d = sqrt(10000 + 0) d = sqrt(10000) d = 100

4. Distance between point D(315, 6) and point E(0, 0): - Using the distance formula: d = sqrt((315 - 0)^2 + (6 - 0)^2) d = sqrt(315^2 + 6^2) d = sqrt(99225 + 36) d = sqrt(99261) d ≈ 314.97

5. Distance between point D(315, 6) and point K(-1, 2): - Using the distance formula: d = sqrt((315 - (-1))^2 + (6 - 2)^2) d = sqrt(316^2 + 4^2) d = sqrt(99856 + 16) d = sqrt(99872) d ≈ 316.04

6. Distance between point D(315, 6) and point F(435, 0): - Using the distance formula: d = sqrt((315 - 435)^2 + (6 - 0)^2) d = sqrt((-120)^2 + 6^2) d = sqrt(14400 + 36) d = sqrt(14436) d ≈ 120.07

So, the distances between the given points are approximately: - A to the origin: 7.62 units - B to the origin: 10.63 units - C to the origin: 100 units - D to E: 314.97 units - D to K: 316.04 units - D to F: 120.07 units

Please let me know if there's anything else I can help you with!