SME
Grade 10 Math · Problem type
Midpoint with an unknown
Use this for “M is the midpoint of AC, AM = 3x + 1 and MC = 5x − 7. Find x, AM and AC.”
Diagram
AC = 26
This is an example. Type your own values to start a new problem.
p
x
+
q
=
r
x
+
(
s
)
The left side is AM’s expression and the right side is MC’s.
x
x
worked out (not typed)
AM
AM
worked out (not typed)
AC
AC
worked out (not typed)
Formulas
p
×
x
+
q
=
r
×
x
+
s
3 × 4 + 1 = 5 × 4 + (−7)
AM
=
p
×
x
+
q
13 = 3 × 4 + 1
AC = 2 × AM
26 = 2 × 13
Assumptions
•
M is the midpoint, so AM = MC: set the two expressions equal and solve for x.
•
Put x back into AM, then AC is twice AM.
•
A length can’t be 0 or less, so check AM is positive.
Step-by-step
WE KNOW
p = 3, q = 1, r = 5, s = −7
FIND
x (x), AM (AM), AC (AC)
Step 1 · Find x (x)
Use p × x + q = r × x + s
Take
the
smaller
x
term
from
both
sides,
then
the
number
beside
the
x
left,
then
divide.
x
=
q
−
s
r
−
p
x
=
1 − (−7)
5 − 3
Take
3
x
from
both
sides:
1
=
2
x
−
7
Add
7
to
both
sides:
8
=
2
x
Divide
both
sides
by
2:
x
=
4
x
=
4
Step 2 · Find AM (AM)
Use AM = p × x + q
Put
x
back
into
AM.
AM = 3 × 4 + 1
AM = 12 + 1
AM = 13
Step 3 · Find AC (AC)
Use AC = 2 × AM
M is the middle, so AC is twice AM.
AC = 2 × 13
AC = 26
Check
Put the numbers back in. Both sides should match.
3 × 4 + 1 = 5 × 4 − 7 ✓
13 = 3 × 4 + 1 ✓
26 = 2 × 13 ✓
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