### Examples

*Example*: The line

*x*+2

*y*=10 is tangent to a circle whose center is located at (2,-1). Find the tangent point and a second tangent point of a line with the same slope as the given line.

*Example*: Given *M*(-4,7) and *N*(12,-1),find the coordinates of point *P* on so that P partitions in the ratio 2:3.

### Clarifications

*Clarification 1*: Problems involving lines include the coordinates of a point on a line segment including the midpoint.

*Clarification 2*: Problems involving circles include determining points on a given circle and finding tangent lines.

*Clarification 3*: Problems involving triangles include median and centroid.

*Clarification 4*: Problems involving quadrilaterals include using parallel and perpendicular slope criteria.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Perspectives Video: Professional/Enthusiast

## MFAS Formative Assessments

Students are asked to find the coordinates of the centroid when given the ratio of a directed segment.

Students are given the coordinates of the vertices of a quadrilateral and are asked to determine whether the quadrilateral could also be a parallelogram, rhombus, rectangle, square, or trapezoid.

Students are given the coordinates of three of the four vertices of a rectangle and are asked to determine the coordinates of the fourth vertex and show the diagonals of the rectangle are congruent.

Students are asked to prove that the quadrilateral formed by connecting the midpoints of the sides of a given quadrilateral is a parallelogram.

Students are asked to find the coordinates of a point which partitions a segment in a given ratio.

Students are asked to prove that two parallel lines have equal slopes.

Students are asked to prove that two lines with equal slopes are parallel.

Students are asked to prove that the slopes of two perpendicular lines are both opposite and reciprocal.

Students are asked to prove that if the slopes of two lines are both opposite and reciprocal, then the lines are perpendicular.

Students are given the coordinates of three vertices of a triangle and are asked to use algebra to determine whether the triangle is scalene, isosceles, or equilateral.

## Student Resources

## Perspectives Video: Professional/Enthusiast

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

## Parent Resources

## Perspectives Video: Professional/Enthusiast

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast