<p> Radicals</p><p>Perfect Squares</p><p>Reducing Radicals Simplify (make the radicand as small as possible)</p><p>1) 2) 3) 4) 5) </p><p>Add and Subtract Radicals Simplify 1) 2) 3)</p><p>Multiply and Divide Radicals 1) 2)</p><p>3) 4) </p><p>Simplify a) b) Length of a Line Segment</p><p>How long is AB?</p><p>In general, how long is AB?</p><p>Side Note: |x| absolute value sign (means distance)</p><p>Example: Find the length of |PM|, where P(-2,1) and M(4,-3)</p><p> p. 71 #1a, 5a, 8, 10, 18, 19 Review from Grade 9 Equations of Lines</p><p>Example 1: Write an equation in standard form for the line that passes through the points C(8,2) and D(4,7)</p><p>Example 2: Write the equation of the line perpendicular to 3x + y - 6 = 0 and passing through P(5,2)</p><p>Practice p. 84 #1 - 3 p. 85 #1adgh, 2adgh p. 87 #1, 2 Equation of a Circle</p><p>An equation for the circle with centre at the origin and radius is </p><p>An equation for the circle with centre at (a,b) and radius r is </p><p>______</p><p>Example 1: Consider the circle defined by the equation </p><p>Complete the table of values to help visualize the graph.</p><p>Example 2: Determine an equation for each circle. (a) (b) (c) </p><p>Example 3: For each equation, state the radius of the corresponding circle and give the coordinates of one point on the circle. (a) (b) </p><p>Example 4: Find an equation for the circle that is centred at the origin and passes through (5, 2).</p><p>Example 5: Find an equation for the circle that is centred at (9,-7) and passes through (5, 2).</p><p>Example 6: Determine whether (2, -6) rests on the circle defined by , or is on the inside or the outside of the circle. Midpoint of a Line Segment</p><p>Definition: Midpoint</p><p>Example: Find the midpoint of line segment AB. </p><p>For any two points (x1, y1) and (x2, y2), the midpoint is ... </p><p>Use the formula to find the midpoint of AB again. </p><p>Example: A circle is centred at (5,4). One endpoint of a diameter drawn on the circle is (-1,2). What is the other endpoint of the diameter?</p><p> p. 77 #1aegh, 2, 3, 4, 7, 8, 10, 13 19ad, 20 Geometric Figures</p><p>Formulae: A(x1, y1) B(x2, y2) </p><p>Length Midpoint Slope</p><p>Triangles Quadrilaterals</p><p>Example: Consider A(-1,2), B(0,6), C(8,4), and D(7,0). What kind of quadrilateral is ABCD?</p><p> p. 95 #1-5 Geometric Figures Example 1) Verify that XYZ is a right triangle. 2) Classify the triangle as scalene, isosceles or equilateral.</p><p> p. 96 #12, 13, 20, 25 - 28, 30 Geometric Figures Continued</p><p>Right Bisector</p><p>Example: Find the equation of the right bisector to AB A(5,4) B(-1,2)</p><p>Median</p><p>Example: Find the equation of the median from A in triangle ABC. A(4,1), B(-1,-5), and C(5,-7)</p><p>Altitude</p><p>Example: Find the equation of the altitude from A in triangle ABC. A(4,1), B(-1,-5), and C(5,-7)</p><p>Practice p. 96 #6, 14, 22 Triangle Centres</p><p> geogebra.org</p><p>Centroid –</p><p>Circumcentre –</p><p>Orthocentre –</p><p>Consider triangle A(0,0), B(6,4) , C(12,-4).</p><p>Example 1: Verify that the centroid is (6,0)</p><p>Example 2: Determine the coordinates of the orthocentre.</p><p> p. 96 #15, 16, 18, 21 Distance from a Point to a Line</p><p>Along what line should you walk to reach the road in the shortest distance possible?</p><p>How far are you from the road if you are at P(-1,3) and the road is x + y - 5 = 0?</p><p>1) slope of the road 2) slope of walking line</p><p>3) equation of walking line 4) The point where you hit the road</p><p>5) Distance from you to where you hit the road</p><p>Practice: p103 #1a, 3ae, 4, 8, 9</p>