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6-7: Distance on the Coordinate Plane

6-7: Distance on the Coordinate Plane. 6-7: Distance on the Coordinate Plane. If points like on a vertical or horizontal line, distance is simply done by subtraction Note: Distance is ALWAYS positive. 6-7: Distance on the Coordinate Plane.

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6-7: Distance on the Coordinate Plane

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  1. 6-7: Distance on the Coordinate Plane

  2. 6-7: Distance on the Coordinate Plane • If points like on a vertical or horizontal line, distance is simply done by subtraction • Note: Distance isALWAYS positive

  3. 6-7: Distance on the Coordinate Plane • If the points A & D were connected, we could find their length. • The connection between the points is a hypotenuse of a right triangle. • We could figure out a, b and then use a2 + b2 = c2 • or… we could use the distance formula

  4. 6-7: Distance on the Coordinate Plane • Distance Formula: Given two points (x1, y1) and (x2, y2), the distance d is

  5. 6-7: Distance on the Coordinate Plane • Use the distance formula to find the distance between J(-8, 6) and K(1, -3). Round to the nearest tenth, if necessary.

  6. 6-7: Distance on the Coordinate Plane • You don’t have to use the formula… • Find the distance between A(6, 2) and B(4, -4). Round to the nearest tenth, if necessary. • What is the x distance? 6 – 4 = 2 • What is the y distance? 2 – (-4) = 6 • Use Pythagorean Theorem • 22 + 62 = c2 • 4 + 36 = c2 • 40 = c2 • 6.3  c

  7. 6-7: Distance on the Coordinate Plane • Find the distance between each pair of points. Round to the nearest tenth, if necessary. • M(0, 3) and N(0, 6) • 3 • C(-3, 4) and H(5, 1) • 8.5

  8. 6-7: Distance on the Coordinate Plane • You can use the distance formula to determine if a triangle is isosceles given its vertices. • Determine whether ABC with vertices A(-3, 2), B(6,5) and C(3,-1) is isosceles. • Recall that an isosceles triangle has two equal sides. • Find the lengths of the three sides (AB, BC and AC) and see if at least two of them match. (Next slide)

  9. 6-7: Distance on the Coordinate Plane • A(-3, 2), B(6,5) and C(3,-1) • Distance of AB • Distance of AC • Distance of BC • The triangle is isosceles

  10. 6-7: Distance on the Coordinate Plane • Assignment • Worksheet #6-7

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