Illustrative Mathematics - Geometry - Unit 6 - Lesson 17

By Formative Library

Last updated about 1 year ago

13 Questions

The 3 lines x=3,y-2.5=-\frac{1}{5}(x-0.5), and y-2.5=x-3.5 intersect at point P. 

Find the coordinates of P. Verify algebraically that the lines all intersect at P.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Triangle ABC has vertices at (0,0),(5,5), and (10,1),. Kiran calculates the point of intersection of the medians using the following steps:
Draw the triangle.
Calculate the midpoint of each side.
Draw the medians.
Write an equation for 2 of the medians.
Solve the system of equations.
Use Kiran’s method to calculate the point of intersection of the medians.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Triangle ABC and its medians are shown. 
Write an equation for median AE.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Given A=(1,2) and B=(7,14), find the point that partitions segment AB in a 2:1 ratio.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

A quadrilateral has vertices A=(0,0),B=(4,6),C=(0,12) and D=(-4,6). Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square.

 Do you agree with either of them? Show or explain your reasoning.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

The image shows a graph of the parabola with focus (-3,-2) and directrix y=2, and the line given by y=-3.
 Find and verify the points where the parabola and the line intersect.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

10.

11.

12.

Write 2 equivalent equations for a line with x-intercept (3,0) and y-intercept (0,2).

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

13.

Parabola A and parabola B both have the line y=-2 as the directrix. Parabola A has its focus at (3,4) and parabola B has its focus at (5,0). 

Select all true statements.

The line of symmetry of parabola A is to the right of that of parabola B.

Parabola A is wider than parabola B.

The line of symmetry of parabola B is to the right of that of parabola A.

The parabolas have the same line of symmetry.

Parabola B is wider than parabola A.

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

This lesson is from Illustrative Mathematics. Geometry, Unit 6, Lesson 17. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/6/17/index.html ; accessed 29/July/2021.

IM Algebra 1, Geometry, Algebra 2 is © 2019 Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

These materials include public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.