Questions: The three medians of triangle ABC meet at a single point. What is the point of the centroid? Express all results in fractions.

The three medians of triangle ABC meet at a single point. What is the point of the centroid? Express all results in fractions.
Transcript text: The three medians of $\triangle A B C$ meet at a single point. What is the point of the centroid? Express all results in fractions. (1 point)
failed

Solution

failed
failed

Solution Steps

Step 1: Find the coordinates of the vertices.

The coordinates of the vertices are A(2, 2), B(8, 2), and C(4, 6).

Step 2: Calculate the centroid.

The centroid of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is given by the formula $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$. Substituting the coordinates of A, B, and C, we get: $$ \left(\frac{2+8+4}{3}, \frac{2+2+6}{3}\right) = \left(\frac{14}{3}, \frac{10}{3}\right)$$

Final Answer: The centroid is located at (14/3, 10/3).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
X-rays have a wavelength small enough to image individual atoms, but are challenging to detect because of their typical frequency. Suppose an X-ray camera uses X-rays with a wavelength of 9.24 nm. Calculate the frequency of the X-rays. Be sure your answer has the correct number of significant digits. PHz
failedAnswered
Given the graph of the parent function below, identify the name of the parent function and the domain range of the parent function Linear Function - Domain: (-∞, ∞) Range: (-∞, ∞) Cubic Function - Domain: (-∞, ∞) Range: (-∞, ∞) Cubic Function - Domain: [-∞, ∞] Range: [-∞, ∞] Linear Function - Domain: (-0, ∞) Range: (-∞, 0)
failedAnswered
How does elevation affect average January temperature? The following data reports elevation in feet (x) and average January temperature in degrees Fahrenheit (y) for 10 US cities. (a) Calculate the correlation coefficient, r. Round answer to THREE decimal places. r= type your answer... (b) Does this correlation suggest there is a linear relation between elevation and average January temperature? (For the first answer blank, write Yes or No. For the second answer blank, write greater or less. For the third blank, write the appropriate critical value from Table II.) type your answer..., since the absolute value of the correlation coefficient is type your answer... than the critical value of type your answer.. (c) Find the equation of the regression line. Round slope and y-intercept to THREE decimal places. y= type your answer... x+ type your answer... (d) Use the regression equation to predict the value of y at x=7000 ft. Round answer to one decimal place, if appropriate. If you should not predict, write 'outside scope' in the answer blank. The predicted average January temperature for 7000 ft is type your answer... degrees Fahrenheit. (e) Use the regression equation to predict the value of y at x=800 ft. Round answer to one decimal place, if appropriate. If you should not predict, write 'outside scope' in the answer blank. The predicted average January temperature for 800 ft is type your answer... degrees Fahrenheit.
failedAnswered
A recent article claims that the state of Illinois has low tuition rates for its colleges and universities. Cate decides to research the cost of tuition for different colleges in Illinois. The average tuition in Illinois is 28,950 with a standard deviation of 3,470. Which type of inference test should Cate use? a) One-sample t-test b) Two-way ANOVA c) One-sample z-test d) Chi-squared test for goodness of fit
failedAnswered
Multiply. 3 × 59/100 =