Page 166 - Math Course 2 (Book 1)

The Distance Formula

Use the Distance Formula to Solve
a Problem Side ZX: Z(–3, –3), X(–5, 1)

2
Example d = (x –x ) + (y – y ) 2 Distance Formula
1
2
2
1
(x , y ) = (–3, –3),
1
1
2
GEOMETRY ZX = [–5–(–3)] + [(1 – (–3)] 2 (x , y ) = (–5, 1)
2
2
Find the perimeter of ΔXYZ to the nearest tenth.
2
ZX = (–2) + (4) 2 Simplify.
First, use the Distance Formula to f nd the length of 4 + 16
each side of the triangle. ZX = Evaluate powers.
ZX = 20 Simplify.
y
Y(–2, 4)
X(–5, 1) Then add the lengths of the sides to f nd the perimeter.
20 + 50 + 20 ≈ 4.243 + 7.071 + 4.472
x
0 ≈ 15. 786

Answer The perimeter is about 15.8 units.
Z(–3, –3)

Side XY: X(–5, 1), Y(–2, 4) Real World Example

2
d = (x –x ) + (y – y ) 2 Distance Formula Nikki kicks a ball from a position that is
2 1 2 1 2 yards behind the goal line and 4 yards from the
side line (–2, 4). The ball lands 8 yards past the goal
(x , y ) = (–5, 1),
1
1
2
XY = [–2–(–5)] + (4 – 1) 2 (x , y ) = (–2, 4) line and 2 yards from the same side line (8, 2). What
2 2 distance, to the nearest tenth, was the ball kicked?
2
XY = (3) + (3) 2 Simplify.
XY = 9 + 9 Evaluate powers. R (–2,4) y
XY = 18 Simplify. S (8, 2)

0 x
Side YZ: Y(–2, 4), Z(–3, –3)
2
d = (x –x ) + (y – y ) 2 Distance Formula 2 2 Distance Formula
2 1 2 1 d = (x –x ) + (y – y )
2 1 2 1
(x , y ) = (–2, 4),
1
1
2
YZ = [–3–(–2)] + (–3 – 4) 2 (x , y ) = (–3, –3) 2 2 (x , y ) = (–2, 4),
1
1
d =
[8–(–2)] + (2 – 4)
(x , y ) = (8, 2)
2
2
2 2
2
YZ = (–1) + (–7) 2 Simplify.
2
d = 10 + (–2) 2 Simplify.
YZ = 1 + 49 Evaluate powers.
d = 100 + 4 Evaluate powers.
YZ = 50 Simplify. Simplify.
d = 104
d ≈ 10.2
Answer 10.2 yards
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