Questions: Remember, medians of a triangle are segments connecting a vertex to the midpoint of the opposite side. Find an equation for the line containing one of the medians in the triangle below; just one median, not all three. (Recall that point O, the intersection of the medians, is called the centroid.)

Remember, medians of a triangle are segments connecting a vertex to the midpoint of the opposite side. Find an equation for the line containing one of the medians in the triangle below; just one median, not all three. (Recall that point O, the intersection of the medians, is called the centroid.)
Transcript text: 20. Remember, medians of a triangle are segments connecting a vertex to the midpoint of the opposite side. Find an equation for the line containing one of the medians in the triangle below; just one median, not all three. (Recall that point O , the intersection of the medians, is called the centroid.)
failed

Solution

failed
failed

Solution Steps

Step 1: Find the midpoint of one side.

Let's find the midpoint of side AB. The coordinates of A are (3,1) and the coordinates of B are (13,1). The midpoint formula is ((x₁ + x₂)/2, (y₁ + y₂)/2). Therefore, the midpoint of AB is ((3+13)/2, (1+1)/2) = (8,1). Let's call this point M.

Step 2: Determine the equation of the line connecting the opposite vertex to the midpoint.

The opposite vertex is C(5,7). We now need to find the equation of the line passing through C(5,7) and M(8,1).

The slope of the line CM is (1-7)/(8-5) = -6/3 = -2.

Using the point-slope form of a line, y - y₁ = m(x - x₁), and using point C, we get: y - 7 = -2(x - 5)

Step 3: Simplify the equation.

y - 7 = -2x + 10 y = -2x + 17

Final Answer

y = -2x + 17

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which patient finding indicates the need for home oxygen therapy? Heart rate 72 beats per minute Respiratory rate 24 breaths/min Arterial partial pressure (PaO2) of 50 mm Hg Serum carbon dioxide level 24 mEq / L
failedAnswered
A patient needs 400 mg of erythromycin oral suspension. The label says erythromycin 200 mg / 5 mL. Give choose your answer... mLs.
failedAnswered
For the following scenario, choose the appropriate set of hypotheses: The graduation rate for students at State College had previously been recorded at 75%. A new administrator states that programs are in place that should increase student graduation rates. H0: μ=0.75 H1: μ>0.75 Ho: p=0.75 H1: p>0.75
failedAnswered
Identify the kind(s) of intermolecular forces that would occur between the solute and solvent in an isopropyl alcohol (which is polar and contains an OH group) solution. Check all that apply. dispersion hydrogen bonding ion-dipole dipole-dipole
failedAnswered
The table below shows the cost, C, of selling x cups of coffee per day from a cart. Determine if the relationship is linear, and find the slope of the line. x 0 5 10 50 100 200 C 70.00 72.00 74.00 90.00 110.00 150.00 The relationship is , the slope of the line is (Enter your answer as a decimal).