Unit 6, Lesson 13

Intersection Points

Geometry

Practice

Problem 1

Graph the equations \((x-2)^2+(y+3)^2=36\) and \(x = 2\). Where do they intersect?

<p>Blank coordinate plane with grid, origin O. Horizontal and vertical scale negative 10 to 10 by 2’s.</p>

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Problem 2

Select all equations for which the point \((2,\text- 3)\) is on the graph of the equation.

\(y-3=x-2\)
\(4x+y=5\)
\(y=5x-13\)
\(x^2+y^2=13\)
\((x-2)^2+(y-(\text- 3))^2=25\)
\(y=(x-2)^2+3\)
\(y=x^2-7\)

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Problem 3

The image shows a graph of a parabola with a focus of \((3,4)\) and a directrix \(y=2\), and of a line given by \(y=4\). Find and verify the points where the parabola and the line intersect.

<p>graph of the parabola with focus at 3 comma 4 and directrix y =2, and the line given by y = 4.</p>

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Problem 4

ForLesson 12: It’s All on the Line

Here is a line \(\ell\). Write equations for and graph 4 different lines perpendicular to \(\ell\) .

<p>graph on line L, y intercept of 7 and slope of -1 over 2</p>

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Problem 5

ForLesson 12: It’s All on the Line

Write an equation whose graph is a line perpendicular to the graph of \(y=4\) and that passes through the point \((2,5)\).

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Problem 6

ForLesson 11: Perpendicular Lines in the Plane

Select all lines that are perpendicular to \(y-4 = \text-\frac{2}3 (x+1)\).

\(y=\frac32 x +8\)
\(3x - 2y = 2\)
\(3x + 2y = 10\)
\(y-2 = \text-\frac{2}3 (x-1)\)
\(y=\frac32 x\)

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Problem 7

ForLesson 10: Parallel Lines in the Plane

Select the line parallel to \(3x - 2y = 10\).

\(y-1 = \frac32 (x+6)\)
\(6x + 4y =\text -20\)
\(y =\text- \frac{3}2 x + 2\)
\(y-4 = \frac23 (x+1)\)

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Problem 8

ForLesson 5: Squares and Circles

Explain how you could tell whether \(x^2+bx+c\) is a perfect square trinomial.

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Intersection Points

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Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Lesson 13 Resources