Question

The diagram below shows a right-angled isosceles triangle ABC, where AB = AC. The coordinates of A and B are given. C y B(9, 2) x 0 A(-1, -2) Calculate: a the equation of the line passing through the points A and B b the equation of the line passing through A and C c the length of the line segment BC to 1 d.p. d the coordinates of the midpoints of all three sides of the triangle.

          The diagram below shows a right-angled isosceles triangle ABC, where
AB = AC.
The coordinates of A and B are given.
C
y
B(9, 2)
x
0
A(-1, -2)
Calculate:
a the equation of the line passing through the points A and B
b the equation of the line passing through A and C
c the length of the line segment BC to 1 d.p.
d the coordinates of the midpoints of all three sides of the triangle.

Show more…

The diagram below shows a right-angled isosceles triangle ABC, where
AB = AC.
The coordinates of A and B are given.
C
y
B(9, 2)
x
0
A(-1, -2)
Calculate:
a the equation of the line passing through the points A and B
b the equation of the line passing through A and C
c the length of the line segment BC to 1 d.p.
d the coordinates of the midpoints of all three sides of the triangle.

Added by Kevin S.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Donya Dobbin

07/29/2023

Step 1

Since they are not provided, I will assume some coordinates for them. Let A be (0, 0) and B be (1, 0). Show more…

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The diagram below shows a right-angled isosceles triangle ABC, where AB = AC. The coordinates of A and B are given: Calculate: a the equation of the line passing through the points A and B b the equation of the line passing through A and C c the length of the line segment BC to 1 d.p. d the coordinates of the midpoints of all three sides of the triangle.

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Transcript

00:01 Alright, here we go.

00:02 So we've got an isosceles triangle that looks like this.

00:07 It's a right triangle.

00:09 This is at negative 1 comma negative 2.

00:15 This one is at 9 comma 2.

00:19 Alright, an equation for the line through there.

00:23 We have point -slope forms.

00:24 So y minus, i'm going to use the a point, so y minus a negative 2 is equal to the slope.

00:31 So slope between a and b, rise is 4, run is 10 times x minus negative 1, which is x plus 1.

00:45 Of course, this should be reduced to 2 fifths.

00:49 Then it wants the slope for, or the equation for, whoops, that's incorrect.

00:53 Try that again.

00:55 I'm gonna write an a there.

00:56 There we go.

00:57 It wants the equation for the line for ac, which is at a right angle.

01:02 It's going through the point a still, so y plus 2.

01:07 The slope of a perpendicular line is the opposite reciprocal, so negative 5 over 2, and then that's x plus 1.

01:17 Then it wants the distance of bc.

01:24 Distance here of the hypotenuse.

01:29 This is isosceles triangle, so this side and this side are the same length.

01:32 So all we have to do is find the distance between a b...

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