Question

Find the coordinates of the orthocenter of the triangle with the given vertices: P(−1,2),Q(5,2),R(2,1) 23. Compare the given measures using Theorems 5.12 or 5.13. B. PQ and RQ

Answer 1

To find the coordinates of the orthocenter of a triangle, we first need to calculate the slopes of the lines containing the triangle's sides. Then, we can find the equations of the altitudes passing through each vertex. By solving the system of equations formed by these altitudes, we can determine the point of intersection, which is the orthocenter.

Step-by-step explanation:

To find the coordinates of the orthocenter of a triangle, we first need to calculate the slopes of the lines containing the triangle's sides. Then, we can find the equations of the altitudes passing through each vertex. By solving the system of equations formed by these altitudes, we can determine the point of intersection, which is the orthocenter.

Given the triangle with vertices P(-1,2), Q(5,2), and R(2,1), let's label the sides as a, b, and c. We will find the equations of the altitudes passing through each vertex and calculate their intersection point, which will give us the coordinates of the orthocenter.

Using the slope formula, the slopes of sides PQ, QR, and RP are 0, -1, and 3, respectively. The equations of the altitudes passing through vertices P, Q, and R are y = 2, x = 5, and y = -3x + 5, respectively. Solving this system of equations, we find that the orthocenter has the coordinates (5,2).

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