In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY .

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In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY .

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In the skateboard design, VW bisects XY at point T , and XT = 39.9 cm . Find XY .

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Skateboard

In the skateboard design, VWbisects XYat point T, and XT=39.9cm. Find XY.

Point Tis the midpoint of XY . So, XT = TY = 39.9cm.

EXAMPLE 1

Find segment lengths

SOLUTION

XY = XT + TY

Segment Addition Postulate

= 39.9 + 39.9

Substitute.

= 79.8cm

Add.

ALGEBRA

Point Mis the midpoint of VW. Find the length of VM .

STEP 1

Write and solve an equation. Use the fact that VM = MW.

EXAMPLE 2

Use algebra with segment lengths

SOLUTION

VM= MW

Write equation.

4x–1= 3x + 3

Substitute.

x – 1 = 3

Subtract 3xfrom each side.

x = 4

Add 1 to each side.

STEP 2

Evaluate the expression for VMwhen x =4.

So, the length of VMis 15.

Check: Because VM = MW, the length of MWshould be 15. If you evaluate the expression for MW, you should find that MW = 15.

MW = 3x + 3 = 3(4) +3 = 15

EXAMPLE 2

Use algebra with segment lengths

VM = 4x – 1 = 4(4) – 1 = 15

a.FIND MIDPOINTThe endpoints ofRSare R(1,–3) and S(4, 2). Find the coordinates of the midpoint M.

EXAMPLE 3

Use the Midpoint Formula

SOLUTION

1

,

–

,

M

M

=

2

5

a.FIND MIDPOINTUse the Midpoint Formula.

2

The coordinates of the midpoint Mare

1

5

–

,

2

2

ANSWER

– 3 + 2

1 + 4

2

2

EXAMPLE 3

Use the Midpoint Formula

b.FIND ENDPOINTThe midpoint of JKis M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

EXAMPLE 3

Use the Midpoint Formula

STEP 1

Find x.

STEP 2

Find y.

4+ y

1+ x

1

2

=

=

2

2

ANSWER

The coordinates of endpoint Kare (3, – 2).

EXAMPLE 3

Use the Midpoint Formula

SOLUTION

FIND ENDPOINTLet (x, y) be the coordinates of endpoint K. Use the Midpoint Formula.

4 + y = 2

1 + x = 4

y =–2

x =3

Use the Distance Formula. You may find it helpful to draw a diagram.

EXAMPLE 4

Standardized Test Practice

SOLUTION