the following points are plotted on a coordinate plane (-1.2), (-1.7) and (4.2) if the points are connected by a straight line with shape will they form? A: an acute triangle B: a right triangle C: an obtuse triangle D:a quadrilateral

So what is it?

Did you graph it?

from the first point to the second is VERTICAL
from the first point to the third is HORIZONTAL
so those two lines are at right angles at the first point
so
what kind of triangle is it ?

without graphing I notice that (-1,2) and (-1,7) lie on a vertical line, and

(-1,2) and (4,2) lie in a horizontal line.

so ....

To determine the shape formed by connecting the given points (-1,2), (-1,7), and (4,2), we need to examine the angles formed by the sides of the triangle.

Step 1: Plot the given points on a coordinate plane.
- The point (-1,2) represents the coordinates x = -1 and y = 2.
- The point (-1,7) represents the coordinates x = -1 and y = 7.
- The point (4,2) represents the coordinates x = 4 and y = 2.

Step 2: Connect the points to form a triangle.
- Draw lines connecting (-1,2) to (-1,7), (-1,7) to (4,2), and (4,2) to (-1,2).

Step 3: Determine the types of angles in the triangle.
- Measure each angle formed by the sides of the triangle.
- To do this, use the distance formula to find the length of each side between the points.
- Then, use the law of cosines to find each angle.

If all three angles are less than 90 degrees, the triangle is an acute triangle (A).
If one angle equals 90 degrees, the triangle is a right triangle (B).
If one angle is greater than 90 degrees, the triangle is an obtuse triangle (C).
If any of the angles is larger than 180 degrees, the figure would be a quadrilateral (D).

By following these steps and determining the types of angles, you can identify the shape formed by connecting the given points.