Suggested languages for you:

Americas

Europe

Problem 676

Find the coordinates of the foot of the altitude to side \(\underline{\mathrm{AC}}\) of the triangle whose vertices are given by \(\mathrm{A}(-2,1), \mathrm{B}(4,7)\), and \(\mathrm{C}(6,-3)\). From this, find the length of the altitude and then the area of the triangle.

Expert verified

The foot of the altitude to side AC is point D(5, -\(\frac{5}{2}\)). The length of the altitude is \(\sqrt{\frac{365}{4}}\). Thus, the area of the triangle is \(\frac{1}{2} * 80^\frac{1}{2} * 365^\frac{1}{4}\) square units.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 38

Points \(\mathrm{A}(-4,-2), \mathrm{B}(2,-2), \mathrm{C}(4,3)\), and \(\mathrm{D}(-2,3)\) are the vertices of quadrilateral \(\mathrm{ABCD}\). (a) Plot these points on graph paper and draw the quadrilateral, (b) What kind of quadrilateral is \(\mathrm{ABCD}\) ? (c) Find the area of quadrilateral \(\mathrm{ABCD}\).

Chapter 38

Plot the points \(\mathrm{A}(-2,3), \mathrm{B}(1,5)\) and \(\mathrm{C}(4,2)\) and find the area of \(\triangle \mathrm{ABC}\).

Chapter 38

Find the area of the triangle whose vertices are \(\mathrm{A}(3,2)\), \(\mathrm{B}(7,2)\) and \(\mathrm{C}(6,5)\)

Chapter 38

Find the area of the polygon whose vertices are \(\mathrm{A}(2,2)\), \(\mathrm{B}(9,3), \mathrm{C}(7,6)\), and \(\mathrm{D}(4,5)\).

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner