The Vertices Of A Triangle On A Coordinate Plane Are { (-4,3)$}$, { (3,3)$}$, And { (3,-2)$}$. What Is The Length Of The Side From The Vertex In Quadrant I To The Vertex In Quadrant IV?A. 1 Unit B. 5 Units C. 6 Units D.

by ADMIN 223 views

Introduction

In mathematics, particularly in geometry, the coordinate plane is a fundamental concept used to represent points, lines, and shapes in a two-dimensional space. The vertices of a triangle on a coordinate plane are given as (−4,3){(-4,3)}, (3,3){(3,3)}, and (3,−2){(3,-2)}. In this article, we will focus on finding the length of the side from the vertex in Quadrant I to the vertex in Quadrant IV.

Understanding the Coordinate Plane

The coordinate plane is a Cartesian plane divided into four quadrants by the x-axis and the y-axis. The quadrants are labeled as I, II, III, and IV, starting from the upper right and moving counterclockwise. The vertices of the triangle are located in Quadrant I, Quadrant II, and Quadrant IV.

Identifying the Vertices

The vertices of the triangle are given as (−4,3){(-4,3)}, (3,3){(3,3)}, and (3,−2){(3,-2)}. To find the length of the side from the vertex in Quadrant I to the vertex in Quadrant IV, we need to identify the coordinates of the two vertices.

Calculating the Distance

To calculate the distance between two points on a coordinate plane, we use the distance formula:

d=(x2−x1)2+(y2−y1)2{d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}

where d{d} is the distance between the two points, and (x1,y1){(x_1, y_1)} and (x2,y2){(x_2, y_2)} are the coordinates of the two points.

Applying the Distance Formula

In this case, we need to find the distance between the vertices (−4,3){(-4,3)} and (3,−2){(3,-2)}. Applying the distance formula, we get:

d=(3−(−4))2+(−2−3)2{d = \sqrt{(3 - (-4))^2 + (-2 - 3)^2}} d=(7)2+(−5)2{d = \sqrt{(7)^2 + (-5)^2}} d=49+25{d = \sqrt{49 + 25}} d=74{d = \sqrt{74}}

Simplifying the Answer

To simplify the answer, we can approximate the value of 74{\sqrt{74}} to be around 8.6 units.

Conclusion

In conclusion, the length of the side from the vertex in Quadrant I to the vertex in Quadrant IV is approximately 8.6 units. This is the correct answer among the given options.

Discussion

The discussion category for this problem is mathematics, specifically geometry and coordinate plane. The problem requires the application of the distance formula to find the length of a side of a triangle on a coordinate plane.

Final Answer

The final answer is: 8.6\boxed{8.6}

Introduction

In our previous article, we discussed the problem of finding the length of the side from the vertex in Quadrant I to the vertex in Quadrant IV of a triangle on a coordinate plane. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the topic.

Q: What is the coordinate plane?

A: The coordinate plane is a two-dimensional space that is divided into four quadrants by the x-axis and the y-axis. It is used to represent points, lines, and shapes in a mathematical context.

Q: What are the vertices of a triangle?

A: The vertices of a triangle are the points where the three sides of the triangle meet. In the case of the triangle on the coordinate plane, the vertices are given as (−4,3){(-4,3)}, (3,3){(3,3)}, and (3,−2){(3,-2)}.

Q: How do I identify the quadrants of a coordinate plane?

A: To identify the quadrants of a coordinate plane, you need to determine the signs of the x and y coordinates of a point. If both x and y are positive, the point is in Quadrant I. If x is negative and y is positive, the point is in Quadrant II. If both x and y are negative, the point is in Quadrant III. If x is positive and y is negative, the point is in Quadrant IV.

Q: What is the distance formula?

A: The distance formula is a mathematical formula used to calculate the distance between two points on a coordinate plane. It is given by:

d=(x2−x1)2+(y2−y1)2{d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}

where d{d} is the distance between the two points, and (x1,y1){(x_1, y_1)} and (x2,y2){(x_2, y_2)} are the coordinates of the two points.

Q: How do I apply the distance formula?

A: To apply the distance formula, you need to substitute the coordinates of the two points into the formula and simplify the expression. In the case of the triangle on the coordinate plane, we need to find the distance between the vertices (−4,3){(-4,3)} and (3,−2){(3,-2)}.

Q: What is the final answer?

A: The final answer is approximately 8.6 units.

Q: What is the discussion category for this problem?

A: The discussion category for this problem is mathematics, specifically geometry and coordinate plane.

Q: What are the options for the final answer?

A: The options for the final answer are A. 1 unit, B. 5 units, C. 6 units, and D. 8.6 units.

Conclusion

In conclusion, the Q&A section provides additional information and clarification on the problem of finding the length of the side from the vertex in Quadrant I to the vertex in Quadrant IV of a triangle on a coordinate plane. We hope that this article has been helpful in understanding the topic.

Final Answer

The final answer is: 8.6\boxed{8.6}