Question

HI = 3.9 and HJ = 6.2. Find IJ

JI = 25 and HI = 13. Find HJ
H is the midpoint of IJ and IH = 0.75. Find HJ
H is the midpoint of IJ and IJ = 9.4. Find IH

Answer 1

Part 1)
`IJ=2.3\ units`

Part 2)
`HJ=12\ units`

Part 3)
`HJ=0.75\ units`

Part 4)
`IH=4.7\ units`

Explanation:

Part 1) HI = 3.9 and HJ = 6.2. Find IJ

we have that

I is between H and J

`HJ=HI+IJ`

substitute the given values and solve for IJ

`6.2=3.9+IJ`

subtract 3.9 both sides

`6.2-3.9=IJ`

`2.3=IJ`

Rewrite

`IJ=2.3\ units`

Part 2) JI = 25 and HI = 13. Find HJ

we have that

H is between I and J

`IJ=IH+HJ`

remember that

IH=HI and IJ=JI

substitute the given values and solve for HJ

`25=13+HJ`

subtract 13 both sides

`25-13=HJ`

`12=HJ`

Rewrite

`HJ=12\ units`

Part 3) H is the midpoint of IJ and IH = 0.75. Find HJ

we have that

H is between I and J and H is the midpoint of IJ

so

`IJ=IH+HJ`

`IH=HJ` ----> because H is the midpoint

we have

`IH=0.75\ units`

therefore

`HJ=0.75\ units`

Part 4) H is the midpoint of IJ and IJ = 9.4. Find IH

we have that

H is between I and J and H is the midpoint of IJ

so

`IJ=IH+HJ` -----> equation A

`IH=HJ` ----> equation B

substitute equation B in equation A

`IJ=2(IH)`

substitute the given value and solve for IH

`9.4=2(IH)`

Divide by 2 both sides

`IH=4.7\ units`